AEROPLANE     DESIGN 

By  F.  S.  BARNWELL 
AND 

A  SIMPLE  EXPLANATION 
of  INHERENT  STABILITY 

By  W.  H.  SAYERS 


Third  Impression   ,  .   . 


LONDON 
McBRIDE,  NAST  &  CO. 

1917 


ru7/ 


PRINTED  IN  ENGLAND  BY 
THB   WESTMINSTER  PRESS,  LONDON,    W. 


A  FOREWORD 
BY  C.  G.  GREY,  EDITOR  OF  "  THE  AEROPLANE  " 

SO  many  new  firms  are  now  entering  the  Aero- 
plane Industry,  and  in  consequence  so  many 
trained  engineers  are  for  the  first  time  taking 
a  serious  interest  In  aeronautical  engineering  that 
the  time  seems  opportune  to  publish  a  general 
review   of  the   general   principles   of  aeroplane 
design. 

The  disquisition  on  the  subject,  which  follows 
this  preface,  was  originally  written  by  Mr.  F.  S. 
Barnwell  to  be  read  as  a  paper  before  the  Engineer- 
ing Society  of  Glasgow  University.  It  was 
subsequently  published  in  serial  form  in  "  THE 
AEROPLANE  "  early  in  1915,  and  so  great  and  so 
constant  was  the  demand  for  the  numbers  con- 
taining the  treatise  that  it  has  seemed  worth  while 
to  republish  the  whole  in  the  form  of  a  small  book, 
and  to  append  to  it  a  short  article  by  Mr.  W.  H. 
Sayers  on  the  subject  of  The  Stability  of  Aero- 
planes, which  also  appeared  in  "  THE  AEROPLANE/' 
Mr.  BarnwelFs  remarks  on  design  as  such  will 
be  easily  understood  by  any  constructional  en- 
gineer, and  his  references  to  questions  of  stability 
will  doubtless  be  made  more  understandable  to 
those  engineers  who  have  not  hitherto  studied 
aerodynamics  by  Mr.  Sayers'  simple  explanation 
of  the  why,  wherefore,  and  how  of  stable  aero- 
planes. 

3 

365085 


A  FOREWORD 

It  seems  well  to  make  clear  why  these  two 
writers  should  be  taken  seriously  by  trained  and 
experienced  engineers,  especially  in  these  days 
when  aeronautical  science  is  in  its  infancy,  and 
when  much  harm  has  been  done  both  to  the 
development  of  aeroplanes  and  to  the  good  repute 
of  genuine  aeroplane  designers  by  people  who 
pose  as  "  aeronautical  experts  "  on  the  strength  of 
being  able  to  turn  out  strings  of  incomprehensible 
calculations  resulting  from  empirical  formulae 
based  on  debatable  figures  acquired  from  in- 
conclusive experiments  carried  out  by  persons  of 
doubtful  reliability  on  instruments  of  problematic 
accuracy. 

Certain  British  manufacturers  of  sufficient 
independence  of  character  have  proceeded 
along  their  own  lines  and  have  produced 
aeroplanes  which  remain  unbeaten,  power  for 
power,  by  any  in  the  world  on  the  score  of  sheer 
efficiency.  These  machines— notably  Avro  two-  > 
seater  "  tractor  "  biplanes,  Bristol  single  seater 
biplane  Scouts,  Martinsyde  Scouts,  and  Vicker's 
"  pusher  "  gun-carrier  biplanes — have  done  more 
than  anything  else  to  assure  to  the  Royal  Flying 
Corps  during  1915  that  ascendancy  in  the  air  over 
German  aircraft  which  has  been  such  a  notable 
feature  of  the  war. 

Among  these  machines  the  speediest  of  all  up 
to  the  end  of  1915  was  the  Bristol  Scout,  a  tiny 
tractor  biplane  designed  in  1914  by  Mr.  F.  S. 
Barnwell  (now  a  Captain,  R.F.C.),  with  the 
practical  help  of  Mr.  Harry  Busteed,  an  Australian 
aviator,  now  an  officer  of  the  Royal  Naval  Air 


A  FOREWORD 

Service,  and  at  that  time  in  the  employ  of  the 
Bristol  Co. 

The  fact  that  the  writing  was  done  before  the 
war  acquits  Mr.  Barnwell  of  any  charge  of  dabb- 
ling with  the  pen  contrary  to  military  custom, 
and  his  consent  to  read  the  proofs  of  this  reprint 
was  only  prompted  by  the  instinct  of  self-defence. 

It  is  to  be  noted  that  his  general  method  of 
design  is  approved  by  other  aeroplane  designers 
who  have  been  successful  in  producing  efficient 
and  effective  aeroplanes.  Consequently  the  new 
arrival  in  the  aircraft  industry  may  take  it  that  he 
is  fairly  safe  in  following  that  method. 

Mr.  W.  H.  Sayers,  erstwhile  an  electrical  and 
mechanical  engineer  of  ability  and  experience, 
was  one  of  the  first  properly  trained  engineers  to 
take  an  active  interest  in  aviation.  He  has  been 
intimately  connected  with  the  aircraft  industry 
since  the  earliest  days  of  aeroplanes,  and  has 
worked  indefatigably  both  at  construction  and 
design.  He  made  a  special  study  of  stability  in 
aeroplanes  in  the  days  when  most  of  the  pilots  of 
to-day  had  never  seen  an  aeroplane,  and  when  not 
more  than  a  couple  of  dozen  people  in  this  country 
could  fly.  The  theories  he  then  evolved  by  rule 
of  thumb  have  since  been  proved  mathematically 
correct. 

For  a  considerable  period  he  was  on  the  staff 
of  "  THE  AEROPLANE,"  and  his  ability  to  put 
abstruse  theoretical  ideas  into  easily  understand- 
able language  proved  of  high  value  to  many 
students  of  aviation.  At  the  beginning  of  the  war 
he  joined  the  Royal  Naval  Air  Service,  and, 


A  FOREWORD 

much  as  his  absence  from  the  paper  is  regretted, 
there  is  considerable  consolation  in  knowing  that 
his  practical  knowledge  of  design  and  construction 
has  proved  useful.  He  has  since  been  promoted 
to  Lieutenant,  R.N.V.R.,  and  appointed  for 
technical  duty  with  R.N.A.S.,  so  one  can  only 
hope  that  in  the  future  his  ability  may  be  turned 
to  still  better  account  in  the  King's  Service. 

C.  G.  G. 


PREFACE 
Written  November,  1915. 

THE  contents  of  this  small  book  originated 
as  a  paper  which  was  read  to  the  Glasgow 
University  Engineering  Society  in  the 
winter  of  1914. 

They  were  published  during  January  and 
February  by  my  friend,  Mr.  C.  G.  Grey,  in  his 
paper  "  THE  AEROPLANE/'  without  any  alter- 
ations or  amendments. 

Since  Mr.  Grey  has  considered  it  worth  re- 
publishing  in  boo!  form,  I  have,  at  his  request, 
gone  over  the  proofs  and  made  sundry  alterations 
and  deletions,  most  of  small  moment. 

The  reader  must  bear  in  mind,  therefore,  that 
the  figures  and  constants  quoted  remain  those 
which  seemed  reasonable  at  the  time  of  first 
writing  the  Paper. 

One  or  two  clerical  errors  have  been  corrected, 
a  fair  amount  of  unnecessary  verbiage  cut  out, 
the  empirical  formula  for  Rudder  Area  (on  page 
58)  altered,  and  the  figures  for  Dihedral  angle 
(on  page  62)  slightly  amplified. 

I  regret  that  it  has  not  been  possible  for  me  to 
re-write  entirely  the  sections  on  Lateral  and 
Directional  Stability,  for  these  are  treated  all  too 
scantily  and  inaccurately  even  in  comparison 
with  the  rest  of  work. 

The    original    "  Preliminary    Remarks "   and 


PREFACE 

11  Conclusion  "  are  left  in,  practically  unaltered, 
for  the  excuses  and  apologies  contained  therein 
are  still  more  necessary  now  than  when  the  Paper 
was  first  written. 

F.  S.  BARNWELL. 
Bristol,  9  Nov.,  1915. 


ERROR. — In  Fig.  12,  p.  54,  the  Reaction  on  the 
Tail  is  shown  as  a  downward  force  ;  this  is, 
of  course,  a  mistake,  as  it  would  be  an 
upward  one  for  the  flight  path  shown.  It  has 
not  been  altered  as  this  would  incur  making 
a  new  block,  and  it  does  not  affect  the  ex- 
planation of  the  method. 


PART  I 
PRELIMINARY  REMARKS 

BEFORE  starting  on  my  subject  matter,  I 
wish  to  make  some  excuses  and  apologies 
which  I  trust  the  reader  will  accept.  Aero- 
plane engineering  is  a  young  science  about  which 
most  people  know  very  little  ;  whilst  those  of  us 
who  do  think  we  know  something  about  it  do  not 
know  nearly  as  much  as  we  should  like  to.  So  to 
take  a  small  sub-division  of  aeroplane  design  and 
attempt  to  deal  with  it  accurately  and  fully  would 
probably  be  of  less  interest  to  the  majority  than 
to  attempt  a  sort  of  precis  of  the  whole  subject. 

Hence  in  this  brief  work  I  try  to  deal  with  a 
very  large  subject  in  a  manner  necessarily  dis- 
tinctly sketchy.  Now  it  is  hard,  when  one  must  be 
brief,  to  touch  on  all  essential  points,  to  be  lucid 
and  to  be  academically  accurate.  It  takes  as  much 
time  trying  to  work  out  how  to  express  oneself 
sufficiently  fully,  accurately,  and  yet  briefly  as  to 
plod  straight  on  saying  everything  one  knows,  or 
thinks  one  knows,  about  a  subject,  and,  unfortu- 
nately, I  have  not  been  able  to  give  nearly  as  much 
time  as  I  should  have  liked  to  the  working  out, 
altering  and  correcting  of  this  paper.  Asking 
your  indulgence  therefore  for  what  may  be 
obscure,  for  what  may  be  incorrect,  and  for  what 
may  be  tedious,  I  shall  commence  on  my  subject. 

0  B 


AEROPLANE  DESIGN 

I  shall  start  by  briefly  describing  of  what  wa 
shall  consider  an  aeroplane  to  consist,  limiting 
my  description  to  3  types  (see  Figs,  (la),  (aa), 
and  (sa) ). 

An  aeroplane  we  shall  consider  therefore  as  a 
machine  consisting  of  a  closed-in  body  in  which 
is  a  seat  for  the  pilot  and  (in  machines  other  than 
single-seaters)  a  seat  or  seats  for  a  passenger  or 
passengers.  In  this  body  are  also  the  control 
mechanisms  for  the  motor  and  for  the  movable 
surfaces  of  the  machine.  Mounted  in  or  on  this 
body  are  the  tanks  for  fuel  and  lubricant.  Mounted 
on  either  the  fore  or  aft  end  of  this  body  is  the 
motor,  the  only  type  presently  worth  considering 
being  the  petrol  internal  combustion.  Directly 
coupled  to  the  motor  is  an  air  propeller.  Attached 
to  the  body  are  the  main  lifting  surfaces,  or,  as  I 
shall  henceforth  call  them,  "  Aerofoils/'  Attached 
to  the  underside  of  the  body  is  the  landing  gear. 
Attached  to  the  rear  end  of  the  body  is  the  tail, 
consisting  of  a  fixed  part  called  the  tail  plane,  and 
a  movable  portion  (or  portions)  called  the  elevator 
(or  elevators)  ;  also  attached  to  the  rear  end  of 
the  body  are  the  movable  vertical  rudder  and  (if 
any)  a  fixed  vertical  surface  or  rear  fin. 

This  applies,  of  course,  to  the  case  in  which 
the  engine  and  propeller  are  fixed  to  the  fore  end 
of  the  fuselage  (as  in  Figs.  la  and  2a).  If  (as  in 
Fig.  3a)  the  engine  and  propeller  are  at  the  rear 
end  of  the  fuselage,  then  the  tail  rudder  and  fin 
must  be  attached  to  suitable  outriggers,  which  are 
clear  of  the  propeller  disc. 

You  will  note  that  I  have  described  only  the 

10 


AEROPLANE  DESIGN 


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AEROPLANE  DESIGN 


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AEROPLANE  DESIGN 


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AEROPLANE  DESIGN 

direct-driven  "  tractor  "  monoplane  and  biplane, 
and  the  direct-driven  "  pusher  "  biplane.  I  think 
that  at  present  these  three  types  contain  the 
greatest  number  of  desirable  features,  and  it  is 
not  advisable  in  the  scope  of  this  paper  to  discuss 
further  types,  however  tempting  their  points  for 
future  development  may  appear. 

It  is  necessary  to  consider  now  the  functioning 
of  an  aeroplane  in  the  simplest  conditions  and  to 
arrive  at  the  primary  necessities  for  the  machine's 
fulfilling  these  conditions.  Let  us  consider  an 
aeroplane  of  total  weight,  WT,  travelling  at  some 
uniform  velocity  Vi,  in  a  straight  line  and  horizon- 
tally (Fig.  i). 

The  forces  acting  on  this  machine  are  (i)  its 
weight  vertically  downwards,  (2)  total  "  lift  "  of 
whole  machine  vertically  upwards  (note  here  that 
I  say  advisedly  of  "  whole  "  machine),  (3)  thrust 
of  air  propeller  in  and  along  direction  of  flight,  (4) 
total  head-resistance  of  whole  machine  in  and 
opposite  tq  direction  of  flight. 

For  the  maintenance  of  this  condition  of  straight 
horizontal  flight  it  is  obvious  that  at  this  speed  Vi, 
total  "  lift  "  of  machine  must  be  equal  to  total 
weight,  and  propeller  thrust  must  be  equal  to  total 
head  resistance.  Further,  if,  as  is  most  probable, 
the  line  of  action  of  total  head  resistance  does  not 
coincide  with  that  of  thrust,  then  the  C.G.  (centre 
of  gravity)  of  the  whole  machine  must  be  such  a 
distance  in  front  of  the  line  of  action  of  total  lift  if 
thrust  be  below  head  resistance,  or  behind  if  thrust 
be  above  head  resistance,  that  the  weight-lift 
couple  is  equal  to,  and  of  opposite  sign  to,  the 


AEROPLANE  DESIGN 


AEROPLANE  DESIGN 

thrust-head-resistance  couple.  In  an  ideal  design, 
thrust,  head-resistance,  and  lift  should  all  pass 
through  the  C.G.  and  they  generally  do  so  ap- 
proximately. But  if  it  be  impossible  to  attain 
this,  it  is  preferable  that  thrust  should  be  kept 
as  nearly  as  possible  through  the  C.G.,  or  slightly 
below  it,  and  head-resistance  kept  above  thrust  ; 
but  in  neither  case  should  the  divergence  be 
great. 

It  is  necessary  now  to  consider  these  four  forces 
in  more  detail.  The  total  weight,  WT,  for  any  par- 
ticular machine  is  a  constant — at  least,  we  may 
consider  it  so,  since  in  preliminary  design  one 
always  considers  the  machine  as  fully  loaded. 
The  total  lift,  LT,  is  the  sum  of  several  forces  which 
all  vary  according  to  the  attitude  of  the  machine 
to  its  flight-path,  and  which  also  all  vary  approx- 
imately as  the  square  of  the  speed.  We  shall  con- 
sider it  as  made  up  of  lift  of  aerofoils  LA,  vertical 
reaction  on  body  of  machine  IB,  and  vertical 
reaction  on  tail  of  machine  IT.  I  call  it  "  lift,"  for 
aerofoils  only,  for  it  may  be  a  downward  force  on 
one  or  other,  or  both,  of  the  other  members. 

The  thrust  of  the  air  propeller,  T,  depends 
upon  the  power  given  to  it,  upon  its  efficiency  E, 
upon  its  revolutions  per  second  r,  and  upon  the 
speed  along  the  flight-path  v.  It  is  matter  for 
discussion  later. 

The  total  head-resistance,  RT,  we  shall  consider 
as  the  sum  of  the  horizontal  reactions  upon  the 
aerofoils  (which  we  shall  call  henceforth  "  dyna- 
mic resistance  "  or  "  drift,"  and  denote  by  RA), 
upon  the  body  rB,  upon  the  landing  gear  ro,  and 

16 


AEROPLANE  DESIGN 

upon  the  tail  IT.  We  shall  henceforth  call  total 
head-resistance  minus  "  dynamic  head-resistance/' 
"  residual  head-resistance,"  and  denote  it  by  Rr. 
Having  noted  what  kind  of  machine  we  have 
to  design  and  the  elementary  conditions  necessary 
for  it  to  fly  in  a  straight  line  ;  I  had  better  turn 
next  to  the  consideration  of  our  sources  of  data, 
for  designing  the  various  members  of  the  machine. 


AEROPLANE  DESIGN 

MOTORS. 

The  motor  is  the  most  expensive,  the  most 
important,  and  the  heaviest  single  item,  and  it 
must  be  properly  mounted,  cooled  and  fed. 

It  is  useful  and  convenient  to  prepare  a  table 
of  motors,  as  shown  in  Fig.  2.  In  the  first  column 
we  have  name  and  type  of  motor  ;  in  the  second 
normal  full  b.h.p.  ;  in  the  third,  r.p.s.  of  motor  at 
this  power  ;  in  the  fourth,  weight  of  motor  in 
Ibs.  complete  with  carburetter,  magneto,  piping, 
etc.,  also  radiator  and  water  (if  water  cooled)  ; 
in  the  fifth,  petrol  consumption  in  galls  ./hour  at 
full  normal  power  ;  in  the  sixth,  the  same  for 
lubricant  ;  in  the  seventh,  weight  of  suitable 
mounting  and  suitable  shields  or  "  cowling  "  ; 
in  the  eighth,  weight  of  suitable  air  propeller 
with  coupling  ;  in  the  ninth,  tenth,  eleventh, 
twelfth  and  thirteenth  columns  we  have  total 
weight  of  motor  (complete  as  in  col.  4)  with 
mounting,  cowling,  propeller,  petrol,  lubricant 
and  tanks,  for  2,  4,  6,  8  and  10  hours  running 
respectively,  at  full  normal  power. 

As  to  how  the  figures  in  this  table  are  obtained. 
Weight  of  motor  complete  is  given  us  by  the 
makers,  likewise  the  power,  revs.,  and  petrol  and 
oil  consumption.  The  weight  of  a  suitable  mount- 
ing is  a  matter  of  deduction  from  the  actual 
weights  of  satisfactory  mountings  for  known 
cases.  I  have  assumed  that  weight  of  mounting 
varies  directly  as  weight  of  motor,  and  have  taken 
it  as  i-yth  weight  of  motor  for  a  rotary,  and  i-ioth 
weight  of  motor  for  a  stationary  engine. 

18 


AEROPLANE  DESIGN 


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AEROPLANE  DESIGN 

The  weight  of  "  cowling  "  I  have  taken  as 
varying  as  the  square  root  of  the  weight  of  the 
motor,  and  as  equal  to  twice  square  root  of  weight 
of  motor  for  a  rotary,  and  one-half  this  weight 
for  a  stationary  motor. 

The  weight  of  tanks  I  have  taken  as  varying 
directly  as  the  capacity,  and  as  i-5th  of  the 
weight  of  the  contents  (when  full,  of  course), 
taking  petrol  as  7.2  Ibs.  per  gallon,  and  lubrica- 
ting oil  at  10  Ibs.  per  gallon. 

The  weight  of  propeller  I  have  taken  as  varying 
as  the  square  root  of  the  horse-power  and  as 
numerically  equal  to  three  times  square  root 
horse-power  in  Ibs. 

All  these  weights  are  fair  ones  from  such  data 
as  I  have  come  across.  You  will  understand  that 
they  are  only  approximate,  but  they  are  accurate 
enough  for  first  estimate  of  weights,  and  probably 
err  on  the  safe,  that  is,  the  heavy,  side. 

From  this  table,  then,  we  can  obtain  the  total 
weight  of  power  plant  for  a  considerable  number 
of  different  powers  and  for  any  length  of  maxi- 
mum power  running  between  the  extreme  limits 
of  present  requirements. 


ao 


AEROPLANE  DESIGN 


AEROFOILS. 

We  must  now  consider  what  results  we  can  get 
from  aerofoils  and  how  to  estimate  the  weights  of 
the  other  members  of  the  machine  before  we  can 
decide  upon  what  motor  to  employ  and  commence 
the  actual  design. 

Data  for  aerofoils  are  founded  entirely  upon 
experimental  work.  I  do  not  think  it  is  possible  to 
calculate  from  first  principles  the  re-actions  upon 
a  body,  of  any  but  the  simplest  forms,  in  an  air 
current,  though,  of  course,  we  can  obtain  by  inter- 
polation and  analysis  many  further  figures  from 
experimentally  determined  bases.  The  method 
almost  universally  employed  is  that  of  suspending 
a  model  in  a  steady  air  current  of  known  direction 
and  velocity,  and  measuring  the  re-actions  and 
moments  upon  it  by  means  of  a  suitable  balance. 

Let  us,  then,  consider  an  aerofoil  moving  at  a 
uniform  velocity  in  still  air,  or,  what  is  equivalent 
as  regards  the  air  reactions  upon  it,  stationary|in 
a  steady  air  current.  (Fig.  3)  Let  us  denote  the 
area  in  square  feet  by  A^the^angle  in  degrees  of  the 


Vfefocty  IT 


:  A  $ 


21 


AEROPLANE  DESIGN 

chord  of  the  wing  section  to  the  relative  air  current 
by  i,  and  the  relative  air  velocity  in  feet  per  sec,  by 
v.  There  is,  of  course,  a  total  resultant  re-action 
RT  upon  this  aerofoil,  which  it  is  most  convenient 
to  measure,  and  consider  as  the  sum  of  two  re- 
actions, one  LA  vertical  to  the  direction  of  the  air 
current,  our  "  lift,"  the  other  RA  along  the  air 
current,  our  "  dynamic  resistance  "  or  "  drift." 
For  convenience  in  varying  A  and  v  these  forces 
are  usually  tabulated  for  different  values  of  i  in 
the  form  of  coefficients.  We  can  write  : 

Lift,  LA  *=•  Ky  Av2  in  Ibs.  weight. 
Drift,  RA  —  Kx  Av2  in  Ibs.  weight, 
for  these  coefficients  of  lift  and  drift,  Ky  and  Kx, 
are  approximately  constant  for  similar  aerofoils 
and  for  the  same  value  of  i  for  all  values  of  A  and 
of  v. 

Our  data  for  aerofoils,  then,  is  based  upon  ex- 
perimentally determined  values  at  different  values 
of  i,  for  the  coefficients  Ky  and  Kx,  and  for  the 
position  of  "  centre  of  pressure,"  or  intersection 
of  line  of  total  resultant  re-action  with  the  chord, 
for  model  size  aerofoils. 

It  is  useful  to  tabulate  the  dynamic  properties 
of  aerofoils  in  the  following  manner  : — For  every 
model  for  which  we  can  get  reliable  data  we  should 
make  on  tracing  cloth  a  standard  sheet.  (Fig.  4). 
On  each  of  these  sheets,  and  in  the  same  position, 
we  draw  an  accurate  scale  section  of  its  aerofoil 
with  a  standard  chord  length  of,  say,  10".  On  each 
sheet,  and  in  the  same  position,  we  also  draw  a 
standard  squared  table  for  its  respective  curves  of 
Ky,  Kx  and  of  locus  of  centre  of  pressure,  with  a 

22 


AEROPLANE  DESIGN 


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AEROPLANE  DESIGN 

base  of  value  for  i  (say,  \"  representing  i°  of  i), 
and  with  ordinate  values  for  both  Ky  and  KJC 
(say,  ¥  representing  .0001  of  Ky  value,  and  2* 
representing  .0001  of  Kx  value).  The  abscissae 
values  should  range  from  —  6°  to  +  30°  for  i,  and 
the  ordinate  values  from  o  to  .002  of  Ky  value. 
That  is  to  say,  our  standard  table  will  be  18* 
long  and  10"  high. 

On  this  table  i"  of  ordinate  value  will  represent 
a  distance  of  centre  of  pressure  from  leading  edge 
of  aerofoil  of  .1  of  chord. 

On  this  same  table  we  draw  a  fourth  curve 


of  t^--    i.e.  fjpvfi     value  on  a  base  of  Ky  value  ; 

Y  of  ordinate  value  representing  unity  for     *f 

value,  and  i"  of  abscissa  value  representing  .0001 
of  Ky  value. 

We  can  now,  by  superimposing  the  sheets, 
compare  any  of  our  aerofoil  forms.  The  sections 
and  tables  will  lie  one  over  the  other,  and  we  can 
see  which  form  gives  us  the  best  Ky  (or  Lift  Co- 
efficient) vajue  at  any  value  of  i,  the  lowest  Kx 
(or  Drift  Coefficient)  vdue  at  any  value  of  i,  the 
least  travel  of  centre  of  pressure,  and  the  highest 

value  for  —^  for  any  value  of  lift  coefficient. 
Drift 

We  must  note  here  that  these  tables  should  all 
be  for  models  of  the  same  plan  form,  i.e.,  of  the 
same  ratio  of  Span  over  Chord  (or  "  Aspect  Ratio") 
and  of  the  same  form  of  ends.  The  National 
Physical  Laboratory  generally  employs  a  standard 

24 


AEROPLANE  DESIGN 

rectangular  plan  form  of  18"  span  and  3"  chord, 
i.e.,  of  Aspect  Ratio  6.  The  coefficient  values  should 
also  (for  absolutely  safe  comparison)  be  for  the 
same  size  of  model  at  the  same  air  speed. 

I  remarked  before  that  these  coefficients  were 
constants  (for  the  same  value  of  i)  for  varying 
values  of  both  A  and  V.  I  must  now,  in  somewhat 
Hibernian  vein,  remark  that  these  "constants  " 
are  not  quite  constant.  The  Ky,  or  lift  coefficient, 
has  been  found  by  experiment  to  be  fairly  con- 
stant for  widely  varying  values  of  A  and  V.  We 
shall  consider  it  as  such,  and  directly  use  model 
Ky  values  for  our  calculations  for  full-sized 
machines,  noting  that  any  error  will  probably  be 
to  the  good.  But  the  Kx,  or  drift  coefficient,  de- 
creases slightly  as  A  increases,  and  also  decreases 
considerably  as  V  increases.  This  has  the  meaning 
that  the  drift  coefficient  of  our  full-size  aerofoil 
will  be  less  than  that  of  the  model,  but  it  also 
means  that  we  cannot  determine  quite  so  accur- 
ately as  we  should  like  to,  what  it  will  be  for  our 
full-size  aerofoil,  especially  if  it  be  for  a  fast  ma- 
chine. 

It  is  most  probable  that  this  difference  is  due 
to  that  part  of  the  total  re-action  caused  by  skin- 
friction,  the  component  of  which  is  small  in  the 
direction  of  lift  but  large  in  the  direction  of  drift  ; 
and  skin-friction  coefficient  we  know  to  increase 
both  with  increase  of  A  and  with  increase  of  V2. 
The  best  thing  that  we  can  do  is  to  use  the  results 
which  the  N.P.L.  gives  us  in  the  latest  report  of 
the  Advisory  Committee.  (See  Fig.  5). 


AEROPLANE  DESIGN 


\ 
PlQ.fi 

/ARlA-noM  or  UrT/bRirr  WITH  LV.   ft 

r^NFLT^of^ 

Lr  Icwtb  of  Chord  ID  Jtxh 

V'  Velodhy  in  fee)-  bev  sex:  . 

/ 

%%^ 

*•  —  &      " 

^ 

m 

^ 

/ 

Sr               «• 

o                  (• 

B                  J 

S             c 

Sr                 3* 

(Fig.  5.)  Here  we  have,  for  several  different  i 
values,  curves  of  lift/drift  on  a  base  of  log  LV, 
where  L  =  length  of  chord  in  feet,  and  V  =  velo- 
city in  feet  per  second.  By  using  this  we  can  from 
model  figures  obtain  fairly  accurately  those  for  a 
full  size  aerofoil  at  any  speed . 

It  is  necessary  now  to  consider  the  effect  of  plan 
form.  (Fig.  6.)  Assuming  first  that  the  plan  form 
of  our  aerofoils  is  rectangular  and  that  we  vary 
the  Aspect  Ratio  only  : 

The  National  Physical  Laboratory  gives  us  this 
table  of  Lift  Coefficient  values,  and  Lift  to  Drift 
values  for  an  aerofoil  of  constant  section  and  of 
Aspect  Ratio  varying  from  3  to  i  to  8  to  i  at 
values  of  i  from — 2°  to  +  2°°-  I  suggest  using 
this  table  comparatively  ;  i.e.,  suppose  we  have 

26 


AEROPLANE  DESIGN 


- sr AW- 


1 
' 


Q.6. 


POR  VARlATKONf  Of  ASPECT  f?AT>0.    (N  pC) 


A*  P£CT     RAT  1  0 


Vl 


Ky       lyb 


L/b 


Ky     Vp 


Ky 


•on 


•044 


i-s 


•OSS' 


2-4 


2-3 


•117 


•loq 


S-2 


6-7 


10-7 


•214- 


•173 


300 


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n-4- 


•246 


•366 


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13-4 


•346- 


•32.0 


lo-i 


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12-7 


•430 


•423 


10-4- 


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11-6 


10-7 


^q£ 


•$16 


£1 


•670 


10-3 


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8-5 


8-3 


•685" 


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662.    3-q 


643     3*7 


4-4 


Ky  yqlo<g.s  i 


blg.  ore  >Q  Abso(/ufej 


fe 


tb.,  foot;  sec.,  upi'te  nou»Hfa/y 


VQlocs  bv   '00236 


figures  for  a  model  of  6  to  i  Aspect  Ratio  and  wish 
to  calculate  its  properties  for  some  other  Aspect 
Ratio,  say,  4  to  i.  We  shall  take  it  that  its  values 
at  4  to  i  will  be  to  its  relative  values  at  6  to  i  as 
are  the  corresponding  values  in  this  table  for  6 
to  i  to  those  for  4  to  i . 

27 


AEROPLANE  DESIGN 

It  appears,  from  such  few  experiments  as 
have  been  made,  that  it  slightly  increases  an 
aerof oil's  efficiency  to  rake  the  ends  somewhat, 
making  the  trailing  edge  longer  than  the  leading 
edge.  This  is  because  such  a  formation  of  ends 
decreases  the  end  losses.  And  probably  the  lower 
the  Aspect  Ratio  the  more  should  the  ends  rake. 
In  practice,  however,  it  is  better  not  to  rake  the 
ends  too  much,  as  we  cannot  then  get  the  best 
distribution  of  stay  attachments  along  both  front 
and  rear  spars. 

I  suggest  about  30°  Rake  for  4  to  i  Aspect 
Ratio,  25°  for  5  to  i,  and  20°  for  6  to  i,  but  these 
are  quite  arbitrary  values. 

From  a  strength  point  of  view  it  is  advant- 
ageous to  taper  the  aerofoils  from  root  to  tip.  But 
as  this  means  a  structure  considerably  more 
difficult  and  costly  to  make,  I  do  not  think  it  is 
quife  justified. 

As  regards  choice  of  Aspect  Ratio  : — For  the 
same  surface,  the  lower  the  Aspect  Ratio  the 
stronger  is  the  aerofoil,  or  the  lighter  for  the  same 
strength,  but  the  lower  will  be  the  maximum 
Lift  to  Drift  value  and  the  maximum  value  for 
Lift.  The  efficiency  at  very  small  and  very  large 
values  for  i  is  not  much  affected,  and,  in  fact, 
appears  from  this  table  to  be  rather  better  for  the 
lower  Aspect  Ratios.  We  must  bear  in  mind  that 
a  low  Aspect  Ratio  is  worse  for  both  lateral  and 
directional  stability  than  a  high  one.  Taking 
everything  into  consideration,  I  would  suggest  5 
to  i  Aspect  Ratio  for  monoplanes  and  small 
biplanes,  and  6  to  i  to  7  to  i  for  large  biplanes. 

28 


AEROPLANE  DESIGN 


lor 

boll)  Lifr  Coefficient- 
UFf/onf^  voluc.  I'r 
byaboul- 


AEROPLANE  DESIGN 

Next,  for  biplanes  only  of  course,  to  consider 
the  effect  of  gap  and  stagger.  Fig.  7.  From  model 
experiments,  we  find  that  the  greater  the  gap  the 
higher  the  efficiency,  whilst  stagger  also  increases 
the  efficiency  somewhat.  The  gap  amount,  how- 
ever, introduces  the  question  of  weight  and  head 
resistance  of  struts  and  stays,  the  greater  the  gap 
the  greater  these  become.  So  we  must  com- 
promise, and  I  should  suggest  a  gap  of  .8  of  Chord 
up  to  equal  to  Chord,  the  smaller  value  for  fast 
and  relatively  high-powered  machines,  the  larger 
for  slower  and  less  highly  powered  ones. 

The  increase  in  efficiency  is  not  very  great  in  a 
staggered  disposition,  and  it  increases  structural 
difficulties,  especially  if  the  means  for  obtaining 
lateral  control  is  by  warping  the  aerofoils.  Stagger 
may,  however,  be  of  considerable  value  for  im- 
proving the  view  obtainable  downwards  from  the 
machine.  Hence,  I  should  suggest  that  the  ques- 
tion of  stagger  should  mainly  depend  upon  the 
disposition  of  the  pilot  and  passenger  in  the 
machine,  noting  that  if  we  use  a  heavy  stagger 
we  should  use  ailerons  and  not  warp. 

We  have  then  data  for  the  dynamic  properties 
of  model  aerofoils  and  know  how  we  can  use 
them  for  calculations  on  full-size  ones. 

Let  us  turn  to  the  consideration  of  the  weight 
of  aerofoils  as  a  structure,  for,  unfortunately, 
they  have  got  to  lift  their  own  weight  first  and 
then  supply  their  surplus  energy  to  lifting  the 
rest  of  the  machine. 


AEROPLANE  DESIGN 


for  Sirpilar  Aerofoils'.  — 

«Cot  UT* 
A  - 


Wr. 


So    ^E-ur*  a^u^gggd^  (^  ttyd?  ^•jpad 


k,  QC 


kt - - 

T   U,  »  -OlA* 


^Fig.  8.)  Similar  structures  will  bear  the  same 
ultimate  load  per  unit  area,  which  means  in  our 
case  that  similar  aerofoils  will  have  the  same 
"  factor  of  safety  "  for  the  same  value  of  useful 
loading  in  Ibs.  per  square  foot. 

Taking  basic  figures  from  actual  satisfactory 
aerofoils,  we  shall  assume  that  we  can  construct 
an  aerofoil  of  100  sq.  ft.  surface,  to  weigh  70  Ibs., 


AEROPLANE  DESIGN 

and  to  stand  5.7  Ibs.  per  sq.  ft.  total  loading  with 
the  margin  of  strength  necessary.  This  figure  for 
weight,  i.e.,  .7  Ibs.  per  sq.  ft.,  includes  the  weights 
of  stays  for  a  monoplane  and  of  stays  and  struts  for 
a  biplane.  Now  we  consider  the  aerofoil  as  stressed 
only  by  the  useful  loading,  i.e.,  total  load,  WT, 
minus  aerofoil  weight,  since  in  flight  it  is  stressed 
only  by  the  lift  it  exerts  over  and  above  its  own 
weight.  We  shall  take  it  then  that  since  the  weight 
of  similar  aerofoils  varies  as  the  cube  of  the  linear 
dimension  and  the  surface  as  the  square,  the 
weight  per  sq.  ft.,  w,  will  vary  as  the  square  root 
of  the  total  surface,  A,  for  the  same  unital  useful 

WT 
loading,  or  value  of  — w. 

Further,  we  shall  take  it  that  for  aerofoils  of  the 
same  total  area,  within  the  limits  of  useful  loading 
desirable  to  employ,  the  weight  per  sq.ft. ,w,  varies 

WT 

directly  as  the  unital  useful  loading  -r-    -  w,  for 

A 

the  same  strength. 

We  see  that  on  these  assumptions  for  a  total 
surface  of  100  sq.  ft.  the  weight  per  sq.  foot  will 
be  .7  Ibs.  for  5  Ibs.  per  sq.  ft.  useful  loading,  but 
for  a  total  surface  of  400  sq.  ft.  it  will  be  1.4  Ibs. 
for  the  same  useful -loading.  This  is  one  of  the 
basic  facts  against  the  building  of  large  sized 
machines  ;  for  unless  we  can  improve  our  structure 
(and  of  course  the  larger  the  machine  the  better 
chance  we  have  of  so  doing)  the  greater  must  the 
proportion  of  aerofoil  weight  to  useful  load  become. 

32 


AEROPLANE  DESIGN 

We  have  then,  that  since 
w  =  k1/x  /  ATlbs.  per  sq.  ft.,  and 

kx  =  .oywhen-^- w  =  5.olbs.per  sq.ft.,and 
k  oc^F  -  w  (useful  loading) 

/"Wx  A 

therefore  kx  =  .014  (    — -  —  w   J 

V  A  / 

and  therefore 

/WT       \ 
w  -  .014^7  A      f  -£-  -  w  J  in  Ibs.  per  sq.  ft. , 

an  equation  for  the  weight  per  sq.  ft.  of  our 
aerofoils,  in  terms  of  total  aerofoil  area  and  total 
weight  of  aeroplane. 


33 


AEROPLANE  DESIGN 


wejqHTS  .,  FIQ  9 
0)  VYfexMroTcuJZ.  u/nUr,  <  c  of 


WO  VY^xuoAi:  oR  SodLw  . 
3     WV  13  * 

dU^til 


-  45O 


of  b- 


ITEM  WEIGHTS. 
We  must  now  get  figures  for  our  other  weights. 

(%•  9-) 

Generally  speaking,  the  size  of  the  Tail,  Rud- 
der, and  Vertical  Fin  (if  used)  will  vary  directly 
as  the  size  of  the  Wings  (this  assumes,  of  course, 
approximately  constant  proportions  for  the 
machine).  I  suggest,  then,  taking  the  necessary 
weight  of  Tail  and  Rudder  and  Fin  as  a  pro- 

Eortion  of  the  aerofoil  total  weight,  and  a  fair 
gure  to  take  is  one-fifth. 

34 


AEROPLANE  DESIGN 

The  weight  of  the  body  introduces  the  question 
of  the  number  of  people  the  machine  is  to  carry. 
A  sufficiently  strong  body  of  the  timber  and  wire, 
fabric  covered,  girder  type  can  be  made,  of  about 
20  ft.  length  and  2  ft.  mean  breadth  and  depth, 
to  weigh  about  90  Ibs.,  i.e.  if  1  —  20  feet,  b  and 
d  =  2  feet  then  WB  =  90  Ibs. 

Since  in  such  a  structure  the  struts  are  (gener- 
ally speaking),  very  strong  compared  to  the  fore 
and  aft  members,  for  the  kind  of  stresses  to  which 
it  is  subjected,  we  shall  assume  that  the  weight 
will  vary  directly  as  the  breadth  and  depth,  but 
as  the  square  of  the  length.  Hence,  we  get  an 
equation  for  weight  of  Body  WB  =»  .057  I3  b  d  in 
Ibs. 

As  for  the  contents  of  this  body.  We  can  seat 
each  person  properly  for  about  10  Ibs.,  and  the 
weight  of  control  mechanism  will  be  from  30  Ibs. 
to  50  Ibs.,  dependent  upon  the  type  employed. 

It  remains  only  to  consider  the  weight  of  suit- 
able landing  gear.  I  think  it  fair  to  consider  the 
weight  of  the  Landing  Gear,  W0,  as  varying 
directly  as  the  total  loaded  weight,  WT,  of  the 
machine,  and  I  think  a  suitable  one  can  be  de- 
signed at  one-fourteenth  of  the  total  loaded  weight 
This  weight  we  shall  take  as  including  the  weight, 
of  the  Tail  Skid.  For  an  average  landing  gear  and 
tail  skid  we  may  consider  weight  of  Tail  Skid 
alone  as  «-  1/20  of  total  weight  of  Landing  Gear. 


35 


AEROPLANE  DESIGN 

FIRST  ESTIMATES. 

We  are  now  in  a  position,  having  been  given 
certain  requirements,  to  make  a  first  estimate  of 
weights,  deciding  in  so  doing  upon  the  motor  to 
employ. 

The  designer  is  generally  required  to  produce  a 
machine  to  carry  a  certain  number  of  people, 
petrol  and  oil  for  so  many  hours'  flight  at  full 
power,  a  certain  weight  of  observing  instruments, 
perhaps  some  weapons  of  offence,  fully  loaded  to 
be  able  to  fly  at  not  less  than  a  certain  maximum, 
and  not  more  than  a  certain  minimum  speed,  and 
to  climb  at  not  less  than  a  certain  minimum  rate. 

Probably  the  simplest  course  to  take  in  this 
brief  outline  of  designing  methods  is  to  assume 
a  certain  set  of  conditions  has  been  given  and 
see  how  we  should  set  about  trying  to  fulfil  it. 
We  shall  assume,  therefore,  that  we  are  asked  to 
design  a  machine  to  carry  two  people,  pilot  and 
passenger,  to  fly  at  80  m.p.h.  maximum  and  40 
m.p.h.  minimum,  to  climb  at  7  feet  per  second 
fully  loaded,  to  carry  petrol  and  oil  for  4  hours, 
to  have  a  good  range  of  view  downwards  for  the 
passenger,  to  carry  a  full  outfit  of  instruments, 
i.e.,  barograph,  compass,  map  case,  watches, 
engines,  revolution  counter,  air  speed  indicator, 
inclinometers,  etc. 

We  must,  of  course,  keep  everything  as  small, 
compact  and  simple  as  possible  to  maintain 
strength  and  avoid  weight. 

To  keep  the  fuselage  weight  and  head  resist- 
ance as  low  as  possible  we  shall  make  it  a  tandem- 
seated  machine. 

36 


AEROPLANE  DESIGN 

As  a  good  downward  view  is  required  for  the 
observer,  we  shall  seat  him  in  front  of  the  pilot 
as  far  forward  as  possible. 

As  the  machine  must  necessarily  be  of  a  fair 
total  weight  and  of  fairly  light  loading  to  fly  at  the 
necessary  minimum  speed,  we  shall  make  it  a 
biplane. 

Further,  we  shall  give  it  sufficient  stagger  for 
the  observer  to  be  able  to  see  vertically,  or  nearly 
vertically,  down  over  the  leading  edge  of  the  lower 
aerofoils. 

This  will  probably  mean  a  rather  large  stagger, 
so  we  shall  decide  on  ailerons  for  lateral  control, 
these  havi,ng  the  further  advantage  over  warping 
that  they  give  much  better  control  power  at  low 
speeds  (which  entails,  of  course,  large  values  of  i). 
Warping  is  equivalent  to  increasing  the  i  value 
of  one  aerofoil  tip  ;  at  slow  speeds  this  may  mean 
no  increased  lift,  as  the  machine  may  already  be 
flying  with  its  aerofoils  at  their  attitude  for  maxi- 
mum lift,  but  it  will  mean  increased  drift  with 
tendency  to  spin  in  the  wrong  direction.  But 
pulling  down  an  aileron  is  equivalent  to  increasing 
the  camber  of  part  of  the  aerofoil,  and,  hence, 
will  give  increased  lift  at  any  value  for  i. 

We  shall  make  the  Body  20  feet  long  by  2  feet 
mean  depth  and  breadth,  and,  therefore,  of  90 
Ibs.  weight,  the  weight  decided  on  before  for  this 
particular  size. 

We  must  allow  350  Ibs.  for  pilot  and  passenger 
in  their  flying  kit,  and  20  Ibs,  for  seating  them. 

The  controls,  being  not  dual  and  being  for 
ailerons,  we  shall  take  at  the  lightest  weight,  30  Ibs. 

37 


AEROPLANE  DESIGN 

For  the  full  kit  of  instruments  called  for  we 
must  allow  30  Ibs. 

This  gives  us  a  total  weight  of  Body  and  con- 
tents of  510  Ibs. 

We  now  come  to  rather  an  impasse,  as  we  cannot 
get  weights  of  Aerofoils,  Tail  Unit  and  Landing 
Gear  until  we  have  fixed  on  the  engine,  and  we 
should  like  to  know  the  total  weight  in  order  to 
fix  on  the  engine.  So  we  must  make  a  first  choice 
of  an  engine,  judging  from  some  previous  machine. 

We  know  that  with  the  80  Gnome  one  can 
make  a  tractor  biplane  to  fly  at  40  to  78  m.p.h. 
with  4  hours'  fuel  and  oil,  pilot  and  passenger, 
and  climb  at  about  the  rate  we  require.  We  shall, 
therefore,  need  more  power  than  the  80  Gnome 
for  our  machine  ;  but,  of  course,  we  want  to  use 
as  low  a  power  as  possible. 

Let  us  try  the  8o-p.h.  Le  Rhone.  From  our 
weight  table  for  engines  we  find  that  total  weight 
for  this  motor  with  4  hours' petrol  and  oil,  tanks, 
mounting,  cowling  and  propeller  will  be  726  Ibs. 

We  now  have  total  weight  less  Aerofoils,  Tail 
Unit  and  Landing  Gear  =  1,246  Ibs.  There  re- 
mains to  fix  on  wing  form  and  loading,  and  thence 
Wing,  Tail  Unit,  and  Landing  Gear  weights. 

The  total  weight  WT  will  be  equal  to  1,246 
Ibs.  +  WG  -(-  (w  x  A)  +  (1/5  w  x  A)  (Fig.  10), 
where  WG  =  weight  of  Landing  Gear,  including 
Tail  Skid,  w  =  weight  of  Aerofoils  in  Ibs,  per 
square  foot,  and  A  =  total  surface  of  Aerofoils 
in  square  feet.  The  1/5  wA  is,  of  course,  the  Tail 
unit  weight. 

Further  we  have  that  WG  =  1/14  WT — 

38 


AEROPLANE  DESIGN 
Hence,  13/14  Wx  —  1246  -f  1.2  wA.  (i) 

£-ST/f\flATTL   fQR  TOTAL  WEIGHT  E.TC  j^q./Q 

To\-Q\  WKcg^f    VVr«  l£46  +u%  -*LtfA  •»--£•  ^A  (Ibs) 
-    J|-WT  =  124-6-1-  I  2  UTA  (lbs)(o 


WE  .  4  |^/0         K/(^0ig  *  •  ooi.q 


Ky  ^  _ 

Ky  por  b^F^S        '2-0* 

Gq/o  -K>  Pborc* 

»  -?5  Ky 


Hg.QCg  !>ece33qry    Model 


Ky  of- 58  R>s-  -ooi^-o 

176 
«q3 


Ky  for  (£0 


ue* 


If  Ky  ftxax  *  -0015-       loadio<^  »  4-3  Ib 
If   WT  «  iqOO  tbo     ^    V£!«4..3!b*/if    .H)€O  A 
UT-  - 


rroro 

UT« 

on, 
froro(0  $00 


Of  WT  -»  iqoolbs 

39 


AEROPLANE  DESIGN 

CHOICE  OF  AEROFOIL 

We  must  now  fix  upon  what  form  of  aerofoil 
to  employ  and  what  loading. 

The  first  thing  to  note  is  that  the  machine  has 
to  be  able  to  fly  at  40  m.p.h.,  or  about  59  f.p.s. 
So  the  maximum  Ky  value  for  the  aerofoils  must 
be  such  as  to  give  us  lift  per  square  foot  at  58  feet 
per  second  equal  to  the  total  loading  per  square 
foot  that  we  shall  choose. 

This  may  seem  a  small  margin  to  allow  for 
obtaining  the  slow  speed,  but  it  must  be  remem- 
bered, that  at  the  slow  speed,  and  consequent 
cabre,  or  tail-down,  attitude  of  the  machine,  there 
will  be  a  certain  amount  of  added  lift  from  the 
tail  and  body  of  the  machine,  and  a  slight  upward 
component  of  propeller  pull. 

Also  we  must  cut  the  slow  speed  as  fine  as 
possible  to  get  the  greatest  possible  high  speed. 

Now,  for  4  Ibs.  per  square  foot,  total  loading  at 
58  feet  per  second  maximum  Ky  must  be  =  .00119 

For  4!  Ibs.  max.  Ky  must  be  =  .00134. 
For  5  Ibs.  max.  Ky  must  be  =  .00149. 
For  5 1  Ibs.  max.  Ky  must  be  =  .00164. 
All  these  being  values  for  a  biplane,  of  course. 


40 


AEROPLANE  DESIGN 

We  must  now  consider  our  high-speed  : 
The  high  speed  is  to  be  80  m.p.h.,  or  117  feet 
per  second.  Considering  it  as  120  feet  per  second 
we  see,  of  course,  that  the  Ky  values  for  this  speed 

-02 

must  be  -j — 2  of  the  Ky  values  for  58  feet  per 


second,  as  loading  is  constant.  That  is  to  say  : 
Ky  at  120  f.p.s.  must  =  .233  Ky  at  58  f.p.s. 


AEROPLANE  DESIGN 

CORRESPONDING  MONOPLANE  VALUES 

We  must  next,  as  our  machine  is  a  biplane,  and 
our  figures  for  model  aerofoils  are  for  single  or 
monoplane  form,  obtain  from  our  tables  for  effects 
of  gap  and  stagger  the  necessary  corresponding 
monoplane  Ky  values.  We  shall  assume  that  we 
shall  make  gap  =  chord  and  stagger  =  about  .4 
of  chord.  We  shall,  therefore,  as  sufficiently  accur- 
ate for  the  present,  take  that  Ky  biplane  =  .85 
Ky  monoplane,  as  it  would  be  about  .82  for  this 
gap  and  no  stagger,  and  we  obtain  about  4  per  cent, 
increase  of  efficiency  due  to  the  stagger. 

That  is  to  say,  the  necessary  biplane  Kys  we 
have  found  for  different  loadings,  must  be  multi- 
plied by  1. 1 8  for  monoplane  tests.  We  get  then  : 

For — 

4.0  Ibs.  per  sq.  ft.  loading  Ky  max.  must  be  .00140 
4-5  »  »  »  »  »  .00158 
5-o  »  »  »  »  »  .00176 

5-5  »  »  »  »  »  -OOI93 
and  Ky  high-speed  =  .233  of  these  values  as  we 

saw  before. 

We  turn  now  to  our  data  sheets  for  Model 
Monoplane  Aerofoils  and  fix  upon  the  best  form 
for  our  case. 

We  have  to  pick  out  that  Aerofoil  which,  having 
a  maximum  Ky  of  .00140  or  over,  will  give  us  the 
highest  value  for  Lift  to  Drift  for  a  Ky  value  = 
.233  of  its  maximum  value  ;  that  is,  we  must  con- 
sult the  curve  of  Ky  value,  and  the  curve  of  Lift 
to  Drift  on  a  base  of  Ky  value,  for  all  our  data 
sheets,  and  pick  out  the  best  Aerofoil  for  this  case. 

42 


AEROPLANE  DESIGN 

We  shall  assume  that  we  have  done  this,  and 
have  found  the  best  Aerofoil  form  for  us  to  be 
one  which  for  a  maximum  Ky  of  .0015  gives  us, 
at  Ky  =  .233  of  .0015  (or  .00035),  a  Lift  to  Drift 
of  10/1, 

With  this  Aerofoil  we  must  have  a  loading  of 
4.3  Ibs.  per  square  foot. 

We  must  now  make  a  shot  at  the  total  weight 
WT,  as  we  shall  then  be  able  to  get  a  figure  for 
total  Aerofoil  Area,  thence  for  Aerofoil  weight, 
thence  a  figure  for  total  weight,  which  must  be 
very  nearly  the  same  as  our  guessed  weight,  or  we 
must  guess  again  with  increased  wisdom. 

We  shall  guess,  then,  that  the  machine  is  going 
to  weigh,  fully  loaded,  i  ,900  Ibs,,  and  it  will,  there- 

1900 
fore,  need  --  ,  or  440  square  feet  of  Aerofoil 

4-3 
surface  at  the  4.3  Ibs.  per  square  foot  total  load- 

ing. 

From  our  previously  determined  equation  : 


We  get  that  w  =  .014^/440  (4.3  -  -  w) 
whence  w  =  .98  Ibs.  per  sq.  ft. 
This,  then,  gives  us  Aerofoil  weight  =  430  Ibs., 

13 
and  we  get  that  —  WT  =  1762,  or  WT  =  1900  Ibs.; 

*4 

of  this,  Tail  unit  weight  is  86  Ibs.,  Landing  Gear 

weight  =136  Ibs.,  and  of  this,  again,  7  Ibs.  is 
Tail  Skid. 

43 


AEROPLANE  DESIGN 

This  is  our  guessed  weight  (I  admit  that  I 
guessed  once  or  twice  in  getting  out  these  figures, 
but  have  spared  you  the  tedium  by  quoting  the 
right  guess  at  once)  ;  so  we  can  take  the  figures 
for  total  weight  and  wing  surface  as  found. 


44 


AEROPLANE  DESIGN 

DEFINITE  DESIGN. 

We  have  now  fixed  weights,  surface,  aerofoil 
form  and  motor,  and  can  proceed  with  the 
design. 

We  shall,  as  this  is  a  largish  machine,  choose  an 
aspect  ratio  of  6  to  i ,  which  gives  us  4  aerofoils  of 
6.15  feet  chord  by  17.5  feet  *  mean  "  span,  which 
with  the  top  centre  plane  of  2  feet  span,  gives  us  a 
total  "  mean  "  span  of  37.0  feet,  and  our  total 
surface  (which  is  surface  of  4  aerofoils  +  top 
centre  plane),  of  440  square  feet.  I  talk  of  ".mean  " 
span,  as  we  shall  employ  ends  raking  at  20°  for 
our  aerofoils. 

We  must  now  draw  out  a  side  elevation  of  the 
body  of  the  machine  with  seats,  tanks,  motor,  and 
tail  skid,  keeping  all  the  weights  as  close  together 
as  possible.  (Fig.  n,  page  46).  We  shall  employ 
a  "  non-lifting  "  Tail  plane,  that  is  to  say,  a  form 
symmetrical  about  its  central  horizontal  plane  and 
with  this  plane  parallel  to  the  axis  of  the  pro- 
peller. 

This  form  is  perhaps  the  safest  to  employ,  as  it 
will  give  no  difference  in  lift  or  depression, 
whether  in  the  propeller  slip  stream  (when  the 
motor  is  running)  or  not  (when  the  motor  is 
stopped).  We  shall  set  the  chord  of  the  aerofoils 
at  3°  to  the  propeller  axis. 

We  now  require  to  place  our  Aerofoils  and 
Landing  Gear,  less  Tail  Skid,  of  course,  on  the 
body  in  such  a  manner  that  the  total  reaction  on 
the  Aerofoils,  at  3°  value  for  i,  passes  through  the 
CG  of  the  whole  machine  (of  this  more  anon),  and 

45 


AEROPLANE  DESIGN 


Fic-.f/. 


JpS*4* 


fitaev&t.  «nerr 


.TABLE  fDR  HORIZONTAL  ^  VERTICAL  CQ 


ITEM 


W 


V2-0 


Motor 


25-0 


4-7 


17  b~ 


13 


IS 


-.2 


Oil 


£2. 


•n-o 


3qo 


10 


2S 


ffetrol  S»TaoK 


•fl-4 


IS30 


Body 


-S 


213 


3o 


IS20 


Piiohs  Scqh 


10 


1430 


toil  SK«d 


138 


2IO7 


IC.08 


-3-c) 


85L2L 


Goaded) 


4-ss^qi 


2234 


w-  w^rf-of  Itertjfo  Ibs 

1  -  Noftx^  d.&h*-of  0|  of  ifenj  /V«fi5  hoe  Y-r . 

X» -      >•        •  '">    X">- 


46 


AEROPLANE    DESIGN 

that  the  centre  of  the  wheel  axle  of  the  Landing 
Gear  is  about  12"  ahead  of  it. 

This,  of  course,  is  another  trial  and  error  pro- 
cess, and  had  best  be  arrived  at  as  follows  : — Draw 
on  a  piece  of  tracing  paper  the  side  elevation  of 
the  Aerofoils  (to  same  scale  as  Body,  of  course), 
with  correct  gap  and  stagger,  also  a  base  line  AB 
inclined  at  3°  to  the  chords.  From  model  figures 
for  the  Aerofoil  form  mark  on  chord  of  each 
Aerofoil  the  position  of  Centre  of  Pressure  with 
1  ^  3°  ;  j°in  these  two  points  by  a  straight  line, 
and  on  this  line  mark  a  point  P,  4/7  of  its  length 
from  the  chord  of  the  lower  Aerofoil  ;  through 
this  point  P  draw  a  line  perpendicular  to  the  afore- 
mentioned base  line  AB.  This  line  we  can  take  as 
representing  accurately  enough  the  line  of  Lift 
reaction  on  our  biplane,  for  i  =  3°.  Through  this 
same  point  P  draw  a  line  parallel  to  the  Base 
line  AB,  which  will  represent  the  line  of  Dyna- 
mic Resistance  of  our  biplane  for  1=3°. 

From  the  figures  for  our  Aerofoil  form,  we  shall 
measure  off,  to  some  suitable  scale,  a  distance 
from  P  on  the  Lift  re-action  line  to  represent  our 
biplane's  Ky  value  i  at  =  3°  and  a  distance  from  P 
on  the  Dynamic  Resistance  line  to  represent  our 
biplane's  Kx  value  at  i  =  3° .  By  drawing  a  parallel- 
ogram and  its  diagonal  through  our  chosen  point  P, 
we  now  get  a  line  (this  diagonal),  which  represents 
the  line  of  Total  Re-action  on  our  Biplane  at  i  =  3° 

Note  that  we  take  4/yths  of  the  inter  Aerofoil 
distance,  not  f,  for  the  top  aerofoil  does  more 
work  than  the  lower,  in  about  the  proportion  of 
4  to  3,  at  small  values  for  i. 

47 


AEROPLANE  DESIGN 

To  same  scale  we  must  draw  on  another  piece 
of  tracing  paper  a  side  elevation  of  the  Landing 
Gear. 

We  must  now  place  these  over  our  body  draw- 
ing in  guessed  positions,  keeping  the  base  line  AB 
on  the  Aerofoil  drawing  parallel  to  the  axis  of 
motor,  and  proceed  to  make  a  first  calculation  for 
position  of  CG.  For  this  calculation  we  shall  take 
horizontal  Moments  about  the  fore  end  of  the 
body,  and  vertical  Moments  about  the  axis  of  the 
motor,  as  convenient  datum  lines,  taking  the 
weights  of  the  various  items  multiplied  by  the 
normal  distances  of  their  CGs  from  these  datum 
lines.  We  can  fix  pretty  accurately  the  CGs  of  the 
items.  I  suggest  taking  the  CG  of  the  Aerofoils  as 
slightly  above  the  centre  of  a  line  joining  the 
centre  points  of  the  lines  which  join  the  centre 
points  of  the  spars  of  top  and  of  bottom  Aerofoils  ; 
slightly  above  (say  n/2oths  above  bottom),  be- 
cause the  centre  plane  and  its  struts  are  at  the  top 
of  the  whole  structure.  The  CG  of  the  body  alone 
may  be  taken  as  about  1/3  of  its  length  from  its 
fore  end  ;  the  CG  of  the  Tail  unit  as  about  i  foot 
ahead  of  the  rear  end  of  the  body  ;  the  CG  of  the 
Landing  Gear,  assuming  a  form  as  shown,  as 
lying  12"  ahead  of,  and  2"  above,  the  wheel 
centres  ;  the  CG  of  a  man  sitting  as  about  12" 
ahead  of  the  seat  back  and  12"  above  the  seat 
bottom. 

The  CGs  of  the  other  items,  tanks  with  petrol 
and  oil,  engine,  engine  mounting,  engine  cow- 
ling, seats,  controls,  instruments,  Tail  Skid,  etc., 
are  easy  to  fix  accurate! v  enough  by  inspection. 

48 


AEROPLANE  DESIGN 

If  our  first  shot  for  Aerofoil  and  Landing  Gear 
position  be  out  we  must  slide  them  to  new  posi- 
tions, and  try  again,  till  we  get  the  positions  which 
answer  our  requirements. 

We  have  now  fixed  up  our  outline  design,  and 
it  remains  to  consider  strength  and  stability,  and 
then  to  finally  check  whether  we  have  sufficient 
power  for  the  high-speed  and  for  the  climb. 

But  before  passing  on  let  us  note  that  the  tank 
positions  must  be  such  that  the  CG  alters  little  in 
horizontal  position,  whether  they  be  full  or  empty, 
and  they  must  also,  of  course,  be  of  the  required 
capacity.  As  it  is  almost  impossible  to  keep  the 
CG  of  both  petrol  and  oil  over  the  CG  of  the 
whole  machine,  and  since  for  our  motor  the  weight 
of  petrol  consumed  per  unit  time  is  about  six 
times  the  weight  of  oil  consumed  per  unit  time, 
we  should  keep  the  CG  of  the  oil  about  six  times 
as  far  (horizontally)  from  the  total  CG  as  is  the 
CG  of  the  petrol,  and,  of  course,  the  tanks  on 
opposite  sides  of  the  total  CG. 

Bearing  this  in  mind,  we  get  in  the  tanks  as 
best  we  can. 


49 


AEROPLANE  DESIGN 

v/ 

WING  STRENGTH. 

For  the  strength  of  the  wings,  considered  as  an 
ordinary  framed  structure,  we  now  have  the  over- 
all sizes,  the  position  of  main  aerofoil  spars  and 
of  struts  and  ties.  Considering  each  spar  as  a  con- 
tinuous beam  and  each  aerofoil  as  uniformly 
loaded  (its  own  weight  being  of  course  now  not 
taken)  for  5/6ths  of  its  mean  length,  we  must  find 
the  curve  of  bending  moments  and  the  reactions 
at  the  supports  of  each  spar,  firstly  with  the  centre 
of  pressure  at  its  position  nearest  to  the  leading 
edge,  and  secondly  at  its  position  for  full  speed, 
which  will  be  much  further  from  the  leading  edge. 
The  sections  and  materials  of  the  spars  must  be 
chosen  such  that  under  neither  of  these  conditions 
do  the  maximum  calculated  fibre  stresses  exceed 
i /6th  of  the  ultimate  compressive  strength  of  the 
material  employed.  This  is  the  so-called  "  factor 
of  safety  "  generally  called  for. 

Similarly  the  cross  sections  and  material  for 
each  strut  must  be  so  chosen  that  (for  a  form  of 
low  head  resistance),  the  maximum  applied  load 
does  not  exceed  i/6th  of  the  ultimate  strength, 
calculated  by  Euler's  formula  for  a  pillar  pin 
jointed  at  both  ends. 

Similarly  each  stay  cable  should  have  an  ulti- 
mate strength,  taking  into  account  any  weakening 
due  to  splicing,  etc.,  of  at  least  6  times  the  maxi- 
mum pull  we  shall,  from  the  before-mentioned 
calculations,  find  it  subjected  to. 

I  suggest  considering  the  aerofoils  as  uniformly 
loaded  for  5/6ths  only  of  their  total  lengths, 

50 


AEROPLANE  DESIGN 

because,  owing  to  end  losses,  the  loading  decreases 
towards  the  outer  ends,  and  this  assumption 
therefore  gives  a  fairly  accurate  and  a  simple 
method  of  accounting  for  the  actual  distribution 
of  loading  over  the  aerofoil  surfaces.  Of  course 
the  uniform  loading  used  for  the  calculation  must 
be  adjusted  so  that  total  loading  remains  equal  to 
the  total  weight  for  stress. 

I  shall  not  touch  further  on  strength  except  to 
say  that  the  same  requirements  hold  throughout 
the  machine,  and  the  unfortunate  designer  is 
expected  to  be  able  to  produce  reasonable  figures 
showing  that  his  detail  design  is  such  that  no  part 
of  the  machine  has  a  "  factor  of  safety  "  of  less 
than  6  under  such  condition,  between  slowest 
and  fastest  flying  speeds,  as  imposes  the  greatest 
strain  on  such  part. 


AEROPLANE  DESIGN 

STABILITY. 

Now  to  consider  stability  and  controllability, 
which  resolves  itself  for  us  into  determining  the 
size  of  Tail  Plane,  Elevator,  Fin,  and  Rudder  and 
amount  of  dihedral  angle  of  the  Aerofoils  for  our 
design. 

The  full  investigation  of  the  stability  of  an  aero- 
plane is  necessarily  an  extremely  long  and  difficult 
process,  involving  mathematics  of  a  high  order.  I 
do  not  propose,  however,  to  consider  anything 
other  than  a  few  very  simple  methods  in  which 
by  using  data  from  model  experiments  and  quite 
elementary  mathematics  we  should  arrive  at 
decently  satisfactory  results.  Thus,  though  they 
are  all  more  or  less  interdependent,  I  propose  to 
consider  longitudinal  or  "  pitching  stability,'* 
lateral  or  "  rolling  stability,"  and  directional  or 
"  yawing  stability  "  separately.  Further,  I  shall 
take  no  account  of  the  moment  of  inertia  of  the 
machine,  though  this  has  effects  on  the  stability > 
except  to  state  that  the  moment  of  inertia  about 
all  three  axes  should  be  kept  as  low  as  possible, 
as  much  from  strength  as  from  stability  consider- 
ations. A  machine  of  large  moment  of  inertia 
may  perhaps  be  made  as  stable  as  one  of  small, 
but,  inasmuch  it  will  rotate  more  slowly  about  any 
axis,  it  is  highly  probable  that  it  will  be  subjected 
to  greater  local  stress  in  a  fluctuating  wind,  and  it 
will  answer  more  slowly  to,  and  is  therefore  more 
likely  to  be  locally  stressed  by,  its  controls. 


AEROPLANE  DESIGN 

LONGITUDINAL  STABILITY. 

First,  then,  for  "  longitudinal  stability,"  and  by 
this  I  mean  an  innate  tendency  of  the  machine  to 
preserve  a  constant  attitude  to  its  flight  path — 
that  is,  to  preserve  a  constant  value  of  i  for  the 
aerofoils.  For  us  this  resolves  itself  into  a  deter- 
mination of  the  size  of  the  tail  plane  and  elevators. 

As  you  will  have  noted  from  our  preceding 
curves  for  aerofoils,  all  along  the  range  of  i  values 
useful  for  flight  a  curved  aerofoil  is  unstable — 
that  is,  as  i  increases  the  CP  moves  forward,  as  i 
decreases  the  CP  moves  backwards  ;  in  both 
cases,  therefore,  the  shift  of  CP  tends  to  aggravate 
and  not  to  stop  the  alteration  of  i  value. 

Similarly,  the  body,  which  for  low  head  resist- 
ance generally  approaches  a  torpedo  form,  is 
instable  for  small  angles  to  its  flight  path.  It  is 
left  to  the  tail,  therefore,  to  counteract  the  in* 
herent  instability  of  aerofoils  and  of  body. 

As  for  the  form  of  calculation,  this  is  best  set 
out  in  tabular  form  (Fig.  12,  page  54).  In  column  I 
we  have  a  values,  a  being  the  angle  which  the  axis 
of  the  motor  makes  with  the  direction  of  flight ; 
in  column  2  the  corresponding  values  for  i,  which 
for  our  case  will  be  a  +  3°  throughout ;  in  column 
3  corresponding  values  for  KY,  the  lift  coefficient 
of  the  aerofoils  ;  in  column  4  corresponding 
values  for  Kx,  the  drift  coefficient  of  the  aerofoils  ; 
in  column  5  values  for  total  reaction  coefficient  R, 

which  is,  of  course,  —  \/KY*  +  Kx* ;  in  column 
6  values  for  A  x  R,  or  aerofoil  surface  multiplied 

S3 


AEROPLANE  DESIGN 


CNJ 


i/7 


a 


F 


CO 


CO 


1 


CO 


IT) 


Si 


F 


^ 


* 


O    gl    • 

b>  tr: 


CO 


54 


AEROPLANE  DESIGN 

by  total  reaction  coefficient  ;  column  7  is  for  L 
values,  L  being  the  perpendicular  distance  from 
CG  of  machine  to  line  of  action  of  R. 

Column  8  is  for  A  x  R  x  L  values,  which  is  a 
function  of  the  moment  of  the  reaction  on  the 
aerofoils  about  the  CG  ;  in  column  9  we  have 
values  of  /3,  or  inclination  of  tail  plane  to  line  of 
flight,  in  our  case  /3,  =  a  throughout  ;  in  column 
10  corresponding  values  of  kY  for  tail  plane  ;  and 
in  column  1 1  corresponding  values  of  kx  for  tail 
plane  ;  in  column  12  values  of  total  reaction 
coefficient  r  on  tail  plane,  r  being,  of  course, 

=  A  /  kya  +  kxa  ;    column  13  is  for  values  of  1, 

perpendicular  distance  from  CG  of  machine  to 
line  of  action  of  r  ;  column  14  for  values  of  r  x  1  ; 
column  15  is  for  values  in  column  9  divided  by 

A  x  R  x  L 

values  in  column  16 — i.e.,  for -. —  — and 

1  x  r 

this  gives  us  the  required  tail  area  necessary  to  just 
counteract  the  moment  of  reaction  on  the  aero- 
foils, assuming  the  tail  as  in  undisturbed  air. 

If  we  can  get  accurate  model  figures  for  the  air 
reactions  on  the  body  of  our  machine  we  should 
get  out  a  second  table,  similar  to  the  foregoing,  to 
find  the  necessary  area  of  the  tail  plane  to  counter- 
act the  instability  of  the  body.  But  as  we  may  not 
have  these  figures,  and  as  the  reaction  on  the 
body  is  comparatively  small  for  a  narrow  form 
such  as  we  are  using,  we  may,  in  the  absence  of 
reliable  model  figures,  neglect  the  second  table, 
and  merely  add  a  small  amount  to  the  tail  surface 
necessary  for  the  aerofoils  alone — say  i/ioth. 

55 


AEROPLANE  DESIGN 

As  to  how  the  figures  for  columns  7  and  13  are 
arrived  at,  in  a  similar  manner  to  that  in  which  we 
drew  the  line  of  total  reaction  on  our  biplane  for 
i  =  3°,  we  must  draw  a  series  of  lines  represent- 
ing lines  of  total  reaction  on  it  for  each  of  the 
i  values  in  the  table.  We  can  then  on  our  side 
elevation  drawing  measure  the  perpendicular 
distances  from  CG  of  machine  to  each  of  these 
lines,  these  distances  being  values  for  L,  to  scale 
of  drawing.  On  the  figure  I  have,  for  clearness, 
only  drawn  line  for  R  at  i'  value  for  i. 

As  for  the  tail  plane,  assuming  we  shall  decide 
to  employ  one  of  the  form  shown,  as  a  good  com- 
promise between  strength  and  efficiency,  if  we 
have  not  figures  for  a  model  of  this  form  it  is 
probably  accurate  enough  to  take  for  it  figures 
for  a  rectangular  plane  of  aspect  ratio  2  to  i . 

As  we  do  not  know  until  after  the  calculation 
the  size  for  our  tail  plane,  we  do  not  know  exactly 
the  position  of  its  line  of  reaction.  But  the  chord 
of  the  tail  plane  is  fairly  small  compared  to  the 
distance  from  CG  of  machine  to  centre  of  pressure 
or  tail  plane,  and  smaller  still  is  the  shift  of  CP  on 
tail  plane  compared  to  this  distance.  Hence  we 
shall  assume  a  point,  say,  2  ins.  above  the  top  of 
the  body  and  2  ft.  from  the  rear  end  of  the  body 
as  the  position  of  C  of  P  on  tail  plane,  and  shall 
neglect  the  shift  of  CP.  Of  course,  if  on  finishing 
the  calculation  we  find  that,  for  the  tail  plane  size 
which  we  shall  need,  our  guess  is  obviously  a  lot 
out,  we  must  alter  up  and  correct  our  table. 

We  shall  take  the  required  area  of  tail  for  our 
machine — that  is  to  say,  area  of  tail  plane  plus 


AEROPLANE  DESIGN 

area  of  elevators — as  twice  the  greatest  area  called 
for  in  the  table.  This  seems  rather  a  libel  on  our 
calculations,  but  the  reason  for  this  apparent  large 
excess  of  tail  area  is  that  the  tail  is  acting  both  in 
the  down-draught  from  the  aerofoils  and — when 
the  engine  is  running — in  the  slip -stream  of  the 
|  propeller  ;  both  of  these  factors  tend  to  decrease 
1  the  alteration  of  air  flow  relative  to  the  tail,  when 
the  attitude  of  the  whole  machine  to  its  flight  path 
is  altered.  That  is  to  say,  they  both  tend  to  decrease 
the  correcting  power  of  the  tail. 

This  figure  of  half-value  for  the  tail  on  the 
machine  to  Tail  considered  as  in  undisturbed  air 
is  approximately  that  found  by  recent  experi- 
ments at  the  N.P.L. 

Before    leaving   the    question    of   longitudinal 
stability  I  would  suggest  that  the  value  of  total 
area  of  tail  should  be  kept  about  as  it  would  be 
found    by    the    foregoing    calculations    for    any 
machine,  but  the  more  the  powyer  of  control  re- 
!  quired   the   greater  should   the   relative   area  of 
elevators  to  tail  plane  be  made.   The  ratio  of 
elevator  area  to  tail  plane  should  lie  between  the 
limits  of  .6  to  .4  and  .3  to  .7.  Outside  these  limits 
we  shall  get  a  machine  either  heavy  on  the  con- 
trols on  the  one  hand,  or  slow  to  respond  on  the 
!  other.  We  shall  use,  therefore,  a  total  area  of  75 
j  sq.  ft.,  of  which  .43,  or  32  sq.  ft.,  is  in  the  elevators, 
and  we  arrive  at  the  sizes  as  shown. 


57 


AEROPLANE  DESIGN 

DIRECTIONAL  STABILITY. 

Very  briefly,  for  "  directional  "  or  "  yawing 
stability,"  for  us  this  now  means  size  of  rudder 
and  fin  required.  I  say  rudder  and  fin  for  our 
machine,  as  I  think  it  is  safer  to  use  a  fin  on  large 
and  heavy  machines.  On  small  and  light  machines 
it  is  perhaps  not  necessary.  Structurally,  of  course, 
the  employment  of  a  fin  is  of  value. 

We  have  at  present  few  figures  on  which  to 
base  calculations  for  rudder  size.  The  rudder 
and  fin  considered  as  a  fixed  surface  must  be  large 
enough  to  counteract  the  inherent  yawing  in- 
stability of  the  body,  also  to  counteract  the  yawing 
effect  of  the  side  surface  of  those  parts  of  the  land- 
ing gear  which  are  ahead  of  the  CG,  and  also  to 
counteract  the  yawing  effect  of  the  propeller 
considered  as  a  front  fin. 

We  must  also  be  sure  that,  when  the  rudder  is 
set  at  about  5  degrees,  say,  it  has  ample  power 
additionally  to  counteract  the  worst  spinning 
moment  induced  by  working  the  warp  or  ailerons. 
Unless  we  have  model  figures  for  yawing  moments 
on  the  fuselage,  and  for  drift  on  an  aerofoil  with 
ailerons  at  different  attitudes,  we  had  better  deter- 
mine our  rudder  area  from  figures  for  other 
machines  as  nearly  like  ours  as  possible  which 
we  know  were  satisfactory  as  regards  their 
directional  stability  and  control. 

I  suggest,  then,  using  an  empirical  formula 

(Fig- 


AEROPLANE  DESIGN 

in  which  s  =»  area  of  rudder  in  sq.ft.,  d  •»  distance 
of  centre  of  area  of  rudder  from  CG  of  machine 
in  feet,  S  is  area  of  side  elevation  of  body,  aero- 
foils, landing-gear,  and  propeller  in  sq.  ft., 
D  =  distance  of  centre  of  this  area  S  behind  CG, 
A  is  area  of  aerofoils  in  sq.  ft.,  and  C  is  a  constant 
which  we  shall  take  as  1.7,  from  figures  for  other 
machines  of  this  type. 


The  value  for  body  side  area  is  the  area  in  side 
elevation  of  body,  complete  with  all  added  top 
superstructure,  cowling  round  motor,  etc. 

The  value  for  side  area  of  aerofoils  is  that  of 
the  aerofoils  with  their  struts  in  side  elevation, 
thus  taking  account  of  the  fin  area  due  to  dihedral. 

In  our^case,  then,  we  have 


1.7  x  •  x  15  «  70  — 


70  x  2.4 


~f-  440  or  s  —  17 


That  is,  we  require  a  rudder  +  Fin  area  of 
17  sq.  ft.  We  shall  dispose  this  in  a  form  as  shown 
in  Fig.  13. 

59 


AEROPLANE  DESIGN 

LATERAL  STABILITY. 

Let  us  consider  the  causes  for  possession  of, 
or  lack  of,  "  lateral  stability  "  in  an  aeroplane. 
An  aeroplane  is  a  body  immersed  in  a  fluid — air 
— and  since  its  average  density  is  very  great  com- 
pared to  that  of  air,  we  consider  it  as  supported 
only  by  the  reaction  of  the  air  upon  its  lifting 
surfaces.  That  is  to  say,  it  is  supported  solely  by 
reason  of  its  speed  relative  to  the  air. 

Now,  for  both  of  the  stabilities  we  have  already 
discussed — that  is  "  pitching  "  stability  and  "  yaw- 
ing "  stability — the  flight  path  is  approximately 
at  right-angles  to  the  axes  of  rotation.  Hence  a 
small  rotation  immediately  induces  a  change  of 
reaction  upon  the  tail  plane,  or  rudder,  as  the  case 
may  be,  which  tends  to  counteract  the  rotation. 
But  when  we  come  to  consider  the  third  form  of 
stability— that  is,  "  lateral  "  or  "  rolling  "  stability 
— we  see  that  the  rotation  now  takes  place  about 
an  axis  which  is  parallel,  or  very  nearly  parallel, 
to  the  flight  path. 

Hence  rotation  about  the  longitudinal  axis,  or 
rolling,  will  by  itself  produce  no  change  whatever 
upon  the  air  reactions  on  the  machine  ;  that  is 
to  say,  if  an  aeroplane  rotate  about  an  axis 
parallel  to  its  flight  path,  no  other  motion  being 
present,  no  force  is  created  to  counteract  the 
rotation. 

However,  when  an  aeroplane  rolls,  other 
movements  do  occur,  and  it  is  from  these  that 
we  attain  "  lateral  stability." 

Let  us  consider,  then  (Fig.  14),  an  aeroplane 

60 


AEROPLANE  DESIGN 


XC; — 


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61 


AEROPLANE  DESIGN 

flying  steadily  and  horizontally  and  assume  that 
some  outside  force,  say  a  puff  of  wind,  rolls  it  over 
slightly.  We  see  that,  as  speed  and  therefore  total 
reaction,  RT,  remain  constant,  and  as  the  lift 
reaction  is  now  out  of  line  with  the  gravitational 
force,  the  vertical  component  of  lift  is  now  less 
than  the  gravitational  force,  and  the  horizontal 
component  is  unbalanced  ;  that  is  to  say,  the 
machine  will  commence  to  drop  and  move  side- 
ways. Directly  it  commences  to  do  this  we  get 
motion  perpendicular  to  the  axis  of  rotation  and, 
if  our  surfaces  are  properly  disposed,  a  righting 
moment  therefrom. 

Briefly,  then,  we  see  that,  for  "  lateral  stability/' 
if  the  machine  had  a  sideways  velocity  relative 
to  the  air,  the  resulting  reactions  on  the  whole 
machine  must  tend  to  raise  the  then  leading  aero- 
foil tip.  This  is  the  main  reason  why  a  dihedral 
angle  for  the  aerofoils  tends  to  give  lateral  stability. 
We  also  see  that,  if  the  outer  shape  of  a  machine 
remain  the  same,  the  higher  the  CG  the  greater 
the  dihedral  we  shall  need,  and  vice  versa. 

It  is  necessary  for  us,  therefore,  to  calculate  the 
vertical  position  of  centre  of  projected  side  area 
of  the  whole  machine  less  the  aerofoils.  I  then 
suggest  that,  if  this  centre  of  area  lie  at  the  same 
height  as  the  CG,  give  3  per  cent,  dihedral  angle 
to  the  aerofoils.  If  the  centre  of  area  lie  above  the 
CG,  less  dihedral  should  be  given  ;  if  below, 
more  dihedral  should  be  given.  For  amount  of 
increment  (or  decrement),  I  suggest  i°  of  dihedral 
per  15  value  (in  sq.  feet  x  feet)  of  vertical  mo- 
ment of  side  area  about  CG.  Theae  figures  are 

62 


AEROPLANE  DESIGN 

quite  arbitrary  ones  and  I  cannot  vouch  for  their 
suitability.  They  approximately  represent  current 
practice  for  machines  of  this  type. 

As  you  will  note,  in  our  design  the  centre  of 
projected  side  area  is  considerably  below  the  centre 
of  gravity,  .55  ft.  ;  so  we  had  better  decide  to 
employ  5  per  cent,  dihedral  angle. 

We  must  note,  before  leaving  the  subject,  that 
too  much  inherent  stability  should  not  be  given 
to  an  aeroplane.  "  Inherent  stability,"  as  I  have 
used  it,  being  a  tendency  of  the  machine  to  retain 
the  same  altitude  to  its  flight  path  or  to  its  relative 
motion  to  the  air,  it  follows  that  the  more  stable  is 
a  machine  in  this  sense  the  more  does  it  tend  to 
follow  alterations  in  wind  direction,  and  this 
quality  in  excess  makes  for  discomfort  in  flying 
and  danger  in  landing.  Hence  we  want  to  ensure 
that  our  machine  has  a  slight  margin  of  stability 
and  that  ample  controlling  power  is  afforded  to 
the  pilot  to  enable  him  to  quickly  alter  at  will  its 
attitude  in  any  direction. 


AEROPLANE  DESIGN 

PROPELLER  THRUST. 

We  have  now  got  our  design  temporarily 
completed  ;  it  remains  to  calculate  the  head  re- 
sistance as  accurately  as  possible  and  the  pro- 
peller thrust,  to  see  if  we  have  sufficient  power 
for  the  reqtiired  high  speed  and  climb  and  to 
check  the  balance  of  the  machine. 

Firstly  for  the  propeller  thrust,  I  cannot  attempt 
to  touch  propeller  design  in  this  paper  ;  it  is  a 
subject  for  many  papers  in  itself.  I  must  merely 
refer  to  experimentally  determined  figures  for 
propellers.  We  have  a  good  many  of  these  and  can 
probably  pick  a  form  that  will  suit  us.  We  will 
take  it,  then,  that  we  have  the  curve  of  efficiency 
for  a  suitable  propeller  on  a  base  of  slip  ratio  at 
constant  revolutions  (Fig.  15). 

The  efficiency  is  expressed,  of  course,  as  — 

Useful  work  Thrust  x  speed 

Total  work                 H.P  given  to  propeller 
/p  x  r\ y 

The  slip  ratio  is  **• where  p  is  pitch  of 

r  p  x  r 

propeller  in  feet,  r  revs,  per  sec.,  and  V  is  speed , 
i.e.,  speed  of  advance  along  axis  in  feet  per  sec. 

Knowing  the  horse-power  our  motor  gives  at 
full  normal  revs.,  we  can  from  this  efficiency 
curve  make  another  curve  of  our  actual  propeller 
thrust  in  Ibs.  on  a  base  of  speed  of  advance,  i.e., 
speed  of  aeroplane,  in  feet  per  sec. 


AEROPLANE  DESIGN 


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65 


AEROPLANE  DESIGN 

HEAD  RESISTANCE. 

It  remains  to  get  figures  for  plotting  a  curve 
of  total  head  resistance  (in  Ibs.)  of  machine  on 
this  same  base  of  speed  in  feet  per  sec. 

For  this  we  turn  to  the  front  elevation  of  our 
aeroplane  (Fig.  16)  and  determine  which  parts 
lie  within  the  propeller  disc  and  which  outside  it. 
The  parts  which  lie  in  the  propeller  disc,  i.e.,  in 
the  slip-stream  from  the  propeller,  will  be  in  a 
current  of  fairly  constant  speed  irrespective  of 
speed  of  machine. 

We  make  our  calculation,  therefore,  in  the  form 
of  two  tables.  The  first  table  is  for  parts  in  the 
slip-stream,  the  second  for  parts  outside  it.  In 
neither  of  these  tables  shall  we  include  aerofoils, 
as  the  total  reaction  on  these  has  already  been 
dealt  with  in  first  balancing. 

The  coefficients  for  resistance  for  the  different 
parts  of  our  machine  we  must  obtain  from  figures 
from  model  experiments,  and  of  these  we  have  a 
fair  armament. 

In  both  tables  we  find  the  resistance  in  Ibs.  for 
each  item  at  some  chosen  fixed  value  of  v  ;  at  the 
same  time  we  take,  as  you  see,  the  moment  of 
resistance  of  each  item  about  the  axis  of  the  motor, 
vertically,  of  course,  in  order  to  obtain  a  figure  for 
vertical  position  of  centre  of  head  resistance. 

We  must  determine  the  vertical  position  of 
Centre  of  head  resistance,  less  aerofoils  of  course, 
to  see  if  there  will  be  a  thrust — head-resistance 
couple.  If  we  find  that  there  is  one — that  is  to  say, 
if  the  line  of  residual  resistance  is  above  or  below 

66 


AEROPLANE  DESIGN 


TABLE  I.      ID 


67 


AEROPLANE  DESIGN 

the  line  of  thrust — we  must  either  (if  practicable) 
alter  the  line  of  thrust  or,  by  slightly  altering  the 
fore  and  aft  position  of  the  aerofoils,  introduce  an 
equal  and  opposite  lift-weight  couple  to  counter- 
act the  thrust-head  resistance  one. 

In  the  first  of  these  tables,  then,  we  shall  take 
V  as  slightly  below  (say  5  per  cent,  below)  the 
pitch  speed  of  the  propeller,  and  we  shall  take  the 
total  resistance  Rx  of  the  items  in  this  table  as  of 
the  amount  thereby  found,  and  as  constant  for  all 
speeds  of  the  machine. 

For  our  case  we  get  Rx  as  67.7  Ibs.  acting  .01 
foot  below  line  of  thrust  and  as  constant. 

In  the  second  table  we  shall  take  V  as  100  f.p.s., 
being  a  convenient  figure  to  work  with,  and  the 
total  resistance  R2  obtained  is,  of  course,  the  re- 
sistance of  all  parts,  except  aerofoils,  outside  the  slip- 
stream at  100  f.p.s.  We  take  R2  as  varying  as  V2. 

In  our  case,  therefore,  we  get  a  second  table 
resistance  R2  of  50.3  Ibs.  at  100  feet  per  sec. — 
that  is  to  say,  R2  =  .00503  v2  Ibs.  and  acts  1.51 
ft.  above  line  of  thrust.  We  see  then  that  for  the 
design  as  so  far  got  out  the  line  of  total  residual 
resistance  is  going  to  be  considerably  above  the 
line  of  thrust.  At  maximum  speed  required,  120 
f.p.s.,  it  is  going  to  be  140.2  Ibs.  acting  .77  foot 
above  the  line  of  thrust.  So  we  must  either  raise 
the  line  of  thrust  or  shift  the  aerofoils  aft  slightly. 
We  should,  however,  make  the  necessary  correc- 
tion for  balance,  for  that  speed  at  which  i  for 
aerofoils  =  3°,  as  then  the  tail  is  floating. 

Now  when  i  =  3°,  Ky  =  .00055,  hence  v  must 
be  88.5  feet  per  sec.,  thence  R,  =  39.5  Ibs.,  and 

68 


AEROPLANE  DESIGN 

thence  total  residual  resistance  R2  +  &2  =  107.2 
Ibs.  and  acts  at  .55  ft.  above  line  of  thrust.  We 
shall  therefore  decide  to  shift  our  line  of  thrust  up 
.6  foot,  which  will  give  a  satisfactory  balance  and 
will  have  the  additional  advantages  of  bringing 
the  line  of  thrust  nearer  to  the  CG  and  of  slightly 
cutting  down  landing  gear  height,  and  therefore 
weight  and  head  resistance. 

We  should  now  correct  our  tables  for  CG  and 
for  residual  head  resistance  ;  this  would  be  a 
repetition  of  the  previously  described  calculations, 
and  the  figures  for  amount  of  total  residual  head 
resistance  which  we  have  already  obtained  would 
hardly  be  altered,  certainly  not  increased,  by  this 
raising  of  line  of  thrust.  Hence,  as  we  can  use 
them  as  they  are  for  looking  into  the  remaining 
points,  I  omit,  for  the  sake  of  brevity,  correcting 
up  these  tables  here. 

Finally,  then,  we  turn  again  to  our  model 
aerofoil  figures  to  obtain  the  remaining  part  of 
the  total  head  resistance,  the  "  drift  "  of  our 
aerofoils  (Fig.  17,  p.  70).  From  the  Ky  values  we 
first  determine  the  speeds  corresponding  to 
several  different  values  for  i,  say  for  i  =  i°,  4°, 
7°,  10°,  13°,  16°. 

Taking  into  account  the  variation  of  lift  to  drift 
with  log  AV  before  quoted,  we  find  then  the  drift 
(RD)  of  our  machine's  aerofoils  at  these  different 
values  for  v. 

By  our  previously  determined  equation  we  find 
the  values  for  part  R2  of  residual  resistance  at 
these  speeds  ;  whilst  part  R!  of  residual  resist- 
ance is  constant  and  already  obtained.  So  now  we 

69 


AEROPLANE  DESIGN 

can  plot  out  our  curve  of  total  resistance,  or  Rx  -f 
R2,  4-  RD. 

If  from  these  curves  of  propeller  thrust  and  of 
total  resistance  now  obtained  we  see  that  the  re- 
sistance be  less  than,  or  equal  to,  the  thrust  at 
the  maximum  speed  we  are  asked  to  accomplish, 
then  this  speed  is,  presumably,  attainable. 


JL 
i 

4 

T 
to 

13 


120 


60 


ros 


T,  (Ibs) 


72 


40 


2* 


18 


17 


Model 


J£4_ 

4f 


roil 


JO  -4- 


2^7 


233 


271 


3J8 


332- 


'»O     HO     120 


L> 

-^ 

\^ 

su 
lo 

/ 

\ 

i 

\ 

70 


AEROPLANE  DESIGN 

CLIMBING  SPEED. 

It  remains  to  find  the  greatest  possible  climb- 
ing speed  and  see  if  the  final  requirement  can  be 
fulfilled. 

The  vertical  height  of  the  thrust  curve  above 
the  total  resistance  curve  at  any  point  along  the 
base  gives  us  the  surplus  thrust  at  the  corres- 
ponding base  line  value  for  speed. 

This  surplus  thrust  multiplied  by  value  for 
speed,  gives  us  a  value  for  foot  Ibs.  per  sec. 
available  for  climbing. 

This  value  we  may  plot  as  a  final  curve  of 
power  available  for  climbing. 

We  then  take  the  maximum  Value  given  us 
by  the  highest  point  on  our  curve),  noting  the 
speed  at  which  this  optimum  value  is  attained. 

Then  our  optimum  value  of  power  for  climb- 
ing -7-  the  total  weight  of  machine  gives  us  best 
climbing  rate  in  feet  per  sec. 

If  this  be  decently  over  the  requirement  we  can 
consider  the  preliminary  design  as  finished. 


71 


AEROPLANE  DESIGN 

IN  CONCLUSION. 

In  the  first  over-all  design,  methods  for  arriving 
at  which  I  have  attempted  to  outline,  no  pains 
should  be  spared  to  get  the  best  and  most  compact 
disposition  of  external  parts,  and  the  best  sizes 
and  forms  for  them.  In  the  structural  design, 
which  I  have  not  touched  upon,  every  detail 
should  be  considered  most  carefully  to  ensure 
that  each  is  as  simple  and  compact,  and,  there- 
fore, as  light  for  its  strength  as  possible,  and  that 
for  each  is  chosen  the  best  material. 

If  this  be  done,  using  with  due  common  sense 
every  source  of  reliable  data,  and  doing  everything 
methodically  and  thoroughly,  it  is  highly  probable 
that  the  results  will  be  good,  and  if  one  goes  on 
working  thus  in  subsequent  designs,  altering  up 
empirical  constants  as  found  necessary  or  advisable 
from  increasing  experience,  one  will  design  better 
machines,  and  will  know  why  they  are  improved. 

It  is  because  this  system  of  methodical  im- 
provement is,  I  think,  the  basis  of  all  true  engineer- 
ing advance,  and  because  little  thrashing  out  of 
tables  and  formulae  has  been  done  so  far  (or  at  any 
rate  published)  from  the  data  presently  available, 
that  I  have  tried  in  this  paper  to  outline  some 
methods  for  doing  so. 

I  am  painfully  aware  that  much  necessary 
matter  has  perforce  been  left  out,  and  that  much  of 
what  I  have  said  is  incorrect,  but  if  it  prove  of  in- 
terest or  instructive,  if  it  help  in  any  way  the  better- 
ment of  this  branch  of  engineering  science,  I  am 
amply  repaid  for  what  time  and  effort  it  has  cost  me. 

72 


PART  II 

A  SIMPLE  EXPLANATION  OF  INHERENT 
STABILITY. 

BY  W.  H.  SAYERS. 

THE  question  of  inherent  stability  is  one 
that  has  attracted  much  interest  and 
caused  much  strife  amongst  all  classes  of 
those  interested  in  aviation.  It  has  been  the  cause 
of  much  activity  on  the  part  of  transcendental 
mathematicians — to  such  effect  that  not  only  have 
they  in  many  cases  bewildered  their  readers  but 
they  are  sometimes  under  suspicion  of  having 
successfully  bewildered  themselves.  It  is  unfor- 
tunately also  the  case  that  many  writers  and 
students  dealing  with  this  question  in  simpler 
language  than  that  of  the  mathematician  have 
been  led  astray  by  the  too  apparently  obvious. 

The  mathematical  treatment  of  such  a  subject 
is  of  great  value,  but  those  capable  of  understand- 
ing the  complex  mathematics  of  others  should 
be  able  to  produce  the  required  results  them- 
selves, provided  they  have  a  clear  vision  of  the 
actual  principles  involved.  Hence  a  simple  straight- 
forward explanation  of  the  actual  known  principles 
by  which  inherent  stability  may  be  attained, 
should  be  of  value  to  both  the  mathematical  and 
the  non-mathematical  reader. 

73  ' 


INHERENT  STABILITY 

It  may  here  be  as  well  to  warn  the  reader  that 
in  all  probability  the  inventors  of  various  inherent 
stability  machines  coming  into  the  classes  which 
will  be  dealt  with  later,  will  deny  that  they  owe 
their  stability  to  the  simple  causes  herein  ex- 
plained, preferring  to  ascribe  their  results  to 
much  more  complicated  phenomena.  It  is  frankly 
admitted  that  the  action  of  certain  stabilising 
devices  is  much  complicated  by  many  curious 
and  incompletely  understood  causes,  but  the 
simple  explanations  herein  given  account  in  the 
main  for  the  general  effects  produced — both 
qualitatively  and  quantitatively — which  corres- 
ponds with  the  eating  of  the  pudding. 


74 


INHERENT  STABILITY 

Before  proceeding  further  it  may  be  as  well  to 
rrive  at  a  clear  understanding  of  what  stability 
leally  is.  We  may  take  as  an  example  the  well- 
i;nown  little  toy,  shown  in  Fig.  i,  consisting  of  a 
Hemisphere  of  lead  surmounted  by  a  paper  cone. 
Placed  in  any  position  it  returns,  immediately  it 
Is  free,  to  the  upright.  As  a  matter  of  fact,  it  goes 
i>ast  the  vertical  position  and  oscillates  slightly 
|>efore  coming  to  rest.  This  quality  is  stability 
jnd  the  stability  is  complete.  It  is  to  be  noticed 
jhat  this  toy,  in  spite  of  its  stability,  requires  only 
j  very  small  disturbing  force  to  move  it  far  from 
jts  original  position,  but  it  returns  very  quickly. 
]  Consider  Fig.  2.  This  shows  a  balance  arm 
laving  on^it  two  equal  sliding  weights.  These 
weights,  being  at  A  equi-distant  from  the  centre, 
nd  having  their  centre  of  gravity  below  the  point 
>f  support  of  the  balance,  the  system  is  in  stable 
quilibrium  and  betrays  the  same  general  charac- 
eristics  as  Fig.  I. 

I  But  move  the  weights  out  to  the  positions  B. 
Oie  system  still  remains  stable,  but  it  will  be 
ound  that  a  much  larger  force  must  be  applied 
o  the  arm  to  produce  a  similar  disturbance — 
•bviously  since  to  move  the  arm  through  the  same 
ngle  the  weights  have  to  be  moved  through  a 
much  greater  distance.  Not  only  this.  After  the 
emoval  of  the  disturbing  force  the  return  to 
jiormal  position  will  be  much  more  sluggish,  and 
!or  small  disturbances  the  system  will  be  steadier, 
jhough  not  more  stable.  This  is  a  point  of  con- 
iderable  importance.  An  aeroplane  having  its 
teavy  parts  distributed  over  a  considerable  space 

75 


INHERENT  STABILITY 

will,  in  the  same  way,  be  slower  to  answer  to  ai; 
disturbances,  and  will  require  more  to  stop  he: 
movements  when  once  started,  but,  owing  partb 
to  the  relative  slowness  of  her  movements,  anc 
partly  to  that  slowness  giving  the  pilot  oppor 
tunity  to  use  his  controls,  will  appear  steadie 
than  a  machine,  otherwise  similar,  having  all  it 
large  weights  closely  concentrated,  and  wil 
generally  be  credited — usually  unfairly — witl 
greater  stability  than  the  livelier  machine. 

Now  the  aeroplane  depends  entirely  on  th 
maintenance  of  its  correct  flight  speed  for  support 
and,  therefore,  inherent  stability  implies  that  th 
machine  possessing  it  shall  always  tend  to  increas 
its  speed,  if  the  speed  is  accidentally  reduced 
This  quality  can  only  be  secured  by  the  action  o 
gravity,  and  acceleration  in  the  line  of  flight  du 
to  gravity  can  only  be  obtained  at  the  expense  o 
a  downward  acceleration. 

Now  it  is  obvious  that  this  accompanying  down 
ward  acceleration,  or  rather  the  motion  due  to  it 
should  be  as  small  as  possible,  as  involuntar 
downward  motion  is  dangerous  if  the  machine  i 
low.  Also,  as  the  ratio  between  the  downwan 
acceleration  and  the  corresponding  horizonto 
one  is  the  angle  of  descent  with  the  motor  stopped 
or  the  gliding  angle  as  it  is  usually  called,  it  is 
matter  of  importance,  even  when  the  machine  i 
high,  as  effecting  the  choice  of  landing  positions 
Hence  the  importance  of  securing,  as  far  as  pos 
sible,  that  stabilising  arrangements  do  not  interfer 
with  the  efficiency  of  the  machine. 

Theoretically,   any   machine   which    possesse 


INHERENT  STABILITY 

he  fundamental  property  of  diving  when  it  has 

ost  its  normal  support  from  any  cause  is  inher- 

ntly  stable,  provided  it  is  properly  balanced  fore 

nd  aft,  for  suppose  such  a  machine  to  turn  over 

ill  its  wings  are  vertical.  It  will  proceed  to  dive 

11  it  attains  a  vertical  speed  equal  to  its  flying 

speed  and  will  then  flatten  out  and  proceed  on  a 

ourse  at  right  angles  to  the  original.  Which  is  to 

ay  that  longitudinal  stability  alone  will  eventually 

ring  a  machine  back  from  even  a  lateral  disturb- 

nee  but  it  will  require  a  considerable  amount  of 

oom  in  which  to  do  so,  as  some,  at  any  rate,  of 

le  forward  velocity  possessed  by  the  machine  at 

le  moment  of  disturbance  is  wasted,  owing  to 

ic  change  of  course  necessary,  which  in  itself  is  a 

urther  objectionable  feature. 

Practically,  therefore,  it  is  desirable  to  correct 
iteral  disturbances  independently  of  longitud- 
lal  ones,  and  in  addition  it  is  well  to  reduce  dis- 
turbances of  all  kinds  as  much  as  possible,  partly 
n  the  score  of  comfort,  but  mainly  to  reduce  the 
>pace  necessary  for  recovery. 
|  A  very  large  number,  in  fact  the  majority,  of 
ixisting  machines  probably  possess  actual  inherent 
lability  in  the  sense  that,  placed  at  a  sufficient 
eight  in  any  position,  they  will,  if  all  the  controls 
re  locked  in  normal  flying  position,  or  in  many 
ases  left  entirely  free,  eventually  assume  their 
ormal  position.  In  most  cases,  however,  a  very 
reat   height   would   be   necessary   for   this   re- 
overy. 

Hence,    practically,    other   qualities    than   the 
;  undamental  longitudinal  stability  are  necessary, 

77 


INHERENT  STABILITY 

and  it  is  convenient  to  consider  the  question  in 
three  divisions  : 

I. — Longitudinal  stability. 
II. — Lateral  stability. 
III. — Directional  stability. 


INHERENT  STABILITY 

LONGITUDINAL  STABILITY 

This  branch  of  the  subject  is  probably  more 
generally  understood  than  any  other,  the  prin- 
ciple of  the  longitudinal  V,  as  it  has  been  termed, 
•  having  been  employed  by  experimental  workers 
in  quite  the  dark  ages.  Fig.  3  shows  the  most 
common  form  in  which  this  principle — that  of 
setting  the  leading  surface  at  a  greater  angle  of 
incidence  than  those  following  it — is  employed 
in  practice.  A  is  the  actual  lifting  surface  of  the 
aeroplane,  which  at  its  normal  angle  of  incidence 
X,  supports  the  whole  machine,  the  centre  of 
pressure  of  A  coinciding  with  the  centre  of  gravity 
of  the  aeroplane.  B  is  the  stabilising  surface  or 
tail,  so  set  as.to  produce  no  lift  at  the  normal  angle. 
Now,  suppose  the  machine  to  pitch  nose  upwards 
through  the  angle  Y.  The  total  lift  on  A  will  not 
increase  greatly,  as  the  extra  resistance  due  to  the 
increased  angle  will  slow  the  machine  down.  (Note 
we  are  assuming  at  the  moment  that  the  machine 
has  just  sufficient  power  for  horizontal  flight). 
The  centre  of  pressure  of  A  wiH  move  forward, 
which  will  tend  still  further  to  increase  the  pitch- 
ing, but  the  tail  surface  B,  instead  of  having  no 
angle  of  attack  and  no  lift,  has  an  angle  Y  and  a 
consequent  lift,  tending  to  swing  the  tail  upwards, 
and  restore  the  normal  position. 

Or,  to  look  at  the  matter  in  another  way,  suppose 
a  machine,  having  two  surfaces  in  tandem  with 
the  weights  so  distributed  that  one  surface  is  much 
more  heavily  loaded  than  the  other,  to  be  in  still 
air  and  with  no  forward  velocity.  Obviously  it  will 

79 


INHERENT  STABILITY 


drop,  and  equally  obviously  the  more  heavily 
loaded  surface  will  drop  faster.  If  this  more  heavily 
loaded  surface  is  the  front  one,  the  machine  takes 
up  a  diving  position  and  picks  up  speed,  and  con- 
sequently begins  to  lift.  Any  arrangement  of 
planes  in  which  the  leading  plane,  or  even  the 
leading  part  of  a  plane,  has  a  greater  angle  of  in- 
cidence than  that  which  follows,  shows  this 
tendency — i.e.,  a  plane  with  a  double  camber — 
the  leading  part  cambered  normally  and  the  trail- 
ing part  cambered  in  the  reverse  way,  may  be  in 

80 


INHERENT  STABILITY 

itself  stable,  and  Fig.  4  shows,  by  the  little  shaded 
sections,  how  a  swept-back  wing  with  a  negative 
tip  provides  in  itself  the  longitudinal  V.  This 
method  of  securing  longitudinal  stability  is  in 
practically  universal  use,  and  actually  produces 
the  desired  result. 

It  is  obvious  that  if  a  machine  in  flight  meets 
an  end-on  gust  its  air  speed  is  momentarily  in- 
creased and  that  it  will  rise  till  its  speed  is  re- 
duced, and  conversely  as  the  gust  dies  away  that 
the  air  speed  falls  and  that  the  machine  must  dive 
to  recover  speed.  These  disturbances  are  essential 
to  the  stability,  but  their  actual  magnitude  may 
be  diminished  by  improvement  of  the  gliding 
angle. 

But  an  end-on  gust  may  produce  other  disturb- 
ances. If  the  centre  of  head  resistance  is  above 
the  centre  of  gravity  of  the  machine,  during  the 
growth  of  the  gust  there  will  be  a  tendency  to 
throw  up  the  nose,  and  during  its  dying  away 
to  dip  the  nose  tending  to  exaggerate  the  move- 
ments which  are  due  to  the  stabilising  force. 
If,  on  the  contrary,  the  centre  of  head  resistance 
is  below  the  centre  of  gravity,  the  forces  will  have 
the  opposite  tendencies,  and  will  oppose  the 
stabilising  forces.  The  latter  condition  is  obviously 
dangerous  and  the  first  is  at  least  objectionable. 
Therefore  it  is  necessary  that  the  centre  of  total 
head  resistance  of  the  machine  should  be  as  nearly 
as  possible  in  the  same  horizontal  line  as  the 
centre  of  gravity,  in  order  that  the  greatest  stabil- 
ising effect  should  be  combined  with  the  least 
disturbance. 

81 


INHERENT  STABILITY 

LATERAL  STABILITY 

Pure  inherent  lateral  stability,  i.e.,  that  form  of 
stability  which  ensures  that,  while  the  flight 
speed  of  the  machine  is  sustained,  it  shall  always 
return  to  an  even  keel  on  the  removal  of  the 
disturbing  force,  is  quite  simply  attainable. 

In  Fig.  5  the  dotted  lines  show  a  pair  of  planes 
with  a  dihedral  in  a  normal  position,  the  full  lines 
show  the  same  planes  tilted  laterally.  As  the  two 
vertical  lines  show,  in  the  tilted  position  there  is 
a  greater  resistance  to  downward  motion  on  the 
low  side  than  on  the  high,  hence  the  high  side  will 
drop  relatively  to  the  low,  till  the  normal  position 
is  regained.  Provided  that  the  centre  of  gravity 
is  not  too  high,  there  will  always  be  a  restoring 
force  with  this  arrangement. 

Fig.  6  may  be  of  some  interest  in  this  connec- 
tion. Here  P!  and  P2  are  the  resultant  pressures 
on  each  half  of  the  wings  at  right  angles  to  the 
planes.  When  the  wings  are  tilted  downwards  to 
the  left,  say,  the  vertical  effect  of  Pl  and  P2  will 
be  slightly  displaced  towards  the  left,  as  shown 
at  L,  acting  through  CL  (the  centre  of  lift),  and 
the  vertical  line  through  CL  will  intersect  a  central 
plane — about  which  the  machine  is  symmetrical 
and  on  which  the  centre  of  gravity  must  lie — at 
some  point  above  the  centre  of  lift,  as  MC.  As 
long  as  MC  is  above  the  centre  of  gravity  the 
machine  is  stable  laterally  and  MC  is  equivalent 
to  the  "  metacentre  "  of  a  ship,  the  vertical  dis- 
tance between  MC  and  CG  being  the  equivalent 
of  metacentric  height.  The  conditions  to  be 

82 


INHERENT  STABILITY 

satisfied  to  provide  simple  lateral  stability  are 
practically  the  same  in  the  two  cases,  and  in  the 
aeroplane  the  provision  of  a  sufficiently  low  CG 
satisfies  them,  even  without  the  dihedral.  Un- 
fortunately, owing  to  the  large  value  of  the  dis- 
turbing forces  (gust  effects,  etc.),  compared  with 
the  supporting  forces,  which  are  also  the  righting 
forces,  and  to  the  fact  that  a  large  disturbance 
will  greatly  diminish  these  supporting  and  right- 
ing forces,  we  have  to  consider  methods  of  re- 
ducing disturbances  in  order  that  recovery  may 
become  quick  and  may  be  completed  before 
striking  the  earth. 

Now  a  machine  is  disturbed  laterally  because 
one  side  gains  lift,  or  the  other  loses  it,  the  side 
having  the  excess  of  lift  rising,  that  having  the 
deficit  falling.  In  a  wing  of  rectangular  plan  form 
— that  is  with  uniform  chord — if  the  pressure  per 
square  foot  is  uniform  it  is  fairly  obvious  that  the 
total  pressure  acts  as  though  it  were  a  single  force 
at  the  centre  of  the  wing,  i.e.,  the  centre  of  pressure 
of  each  wing  is  half-way  along  the  span. 

Fig.  7  shows  a  wing  of  triangular  plan  form, 
tapering  to  a  point.  If  such  a  wing  is  acted  on  by 
a  uniform  pressure  per  square  foot  it  will  be  seen 
that  the  total  pressure  on  any  strip,  say,  i  ft.  wide, 
will  be  proportional  to  the  fore  and  aft  length  of 
that  strip,  and  that  the  pressure  on  longitudinal 
strips  will  be  proportional  to  the  length  of  the 
arrow  under  that  strip  (in  the  lower  part  of  Fig.  7). 
Hence  the  total  resultant  force  will  be  as  the  large 
arrow  (R)  acting  closer  to  the  body  than  halfway. 
Also  if  one  wing  receives  an  excess  pressure  which 

83 


INHERENT  STABILITY 


IN 

1! 

lin 

T   T 

-•  f  ' 

t-7. 

M 

is  uniform  per  square  foot  the  resultant  of  that 
excess  will  act  as  closer  to  the  body,  and  from  the 
well-known  principle  of  the  lever,  will  produce  a 
smaller  effect  on  the  machine. 

Now,  obviously,  any  less  degree  of  taper  will 
produce  a  similar,  though  less,  effect,  and  so  also 
will  reduction  in  the  camber  and  angle  of  inci- 
dence ("  wash  out  ")  from  the  body  to  the  tip, 
for  any  pressure  due  to  air  moving  past  the  wings 
with  a  velocity  in  the  line  of  flight.  That  is,  a 
[<  wash  out  "  would  not  make  any  difference  to 
the  effect  of  purely  vertical  gusts,  if  such  things 
could  exist. 

Now,  consider  a  wing,  tapered  or  washed  out 
so  as  to  bring  the  Centre  of  Pressure  close  to  the 


INHERENT  STABILITY 


body  side,  but  provided  with  an  extension  set  at 
a  negative  angle.  This  extension  produces  a  down- 
ward pressure,  which  diminishes  the  total  pressure 
on  the  wings,  but  also  moves  the  point  of  appli- 
cation, or  centre  of,  total  pressure  closer  still  to 
the  body,  and  since  this  negative  pressure  is  acting 
much  further  out  (at  a  larger  radius)  the  centre 
of  total  pressure  may  be  caused  to  pass  beyond 
the  base  of  the  plane  without  completely  neutral- 
ising the  lift. 

If  we  can  thus  cause  the  centre  of  total  pressure 
of  such  a  wing  to  lie  on  the  centre  line  of  the 
machine  (and  this  is  possible  in  theory  at  any 

85 


INHERENT  STABILITY 

rate),  then  one  wing  will  maintain  the  machine  in 
balance  laterally,  the  other  side  being  absent.  If 
this  condition  is  attained,  then  as  long  as  each 
separate  wing  is  in  uniform  air,  however  different 
may  be  the  conditions  around  each  wing,  no  force 
tending  to  overturn  the  machine  sideways  exists. 
This  condition  does  not  occur,  of  course.  But 
Fig.  8  shows  an  aeroplane  in  a  side  gust.  Since 
the  machine  has  a  forward  movement,  the  actual 
movement  of  the  air  during  the  gust  must  be 
diagonal,  and,  as  the  diagram  shows,  one  wing  is 
practically  unshielded,  i.e.,  if  the  gust  is  uniform 
that  wing  is  subject  to  uniform  conditions,  and 
on  this  wing  the  whole  compensating  effects  of 
negative  tips  would  take  effect,  leading  to  at  least 
a  considerable  reduction  in  the  disturbance.  The 
far  wing  is  partly  and  unequally  shielded,  the 
tips  receiving  the  least  shelter.  The  dotted  lines 
show  that  sweeping  back  the  tips  places  the  far 
side  wing  in  more  nearly  uniform  shelter.  The 
figure  is,  of  course,  diagrammatic  only,  and 
should  not  be  taken  as  representing  that  a  large 
portion  of  the  far  wing  is  completely  shielded — 
were  this  the  case  the  problem  would  be,  indeed, 
hopeless.  In  fact,  with  swept-back  wings  and 
properly  proportioned  negative  tips  the  uncor- 
rected  disturbances  due  to  uneven  shielding  are 
quite  small. 


86 


INHERENT  STABILITY 

VERTICAL  FINS. 

If  the  wings  form  a  dihedral  angle,  then  in 
addition  to  the  extra  lift  caused  by  a  side  gust  on 
the  near  or  unshielded  wing,  there  is  a  tendency 
to  lift  the  near  side  and  depress  the  far  side,  due 
to  the  fact  that  at  right  angles  to  the  line  of  flight 
the  near  wing  has  a  positive,  and  the  far  a  negative, 
angle  of  incidence. 

This  may  be  compensated  for  by  enlarging  the 
negative  tip  surface,  or  by  providing  a  vertical  fin 
below  the  centre  of  gravity,  which  will  produce 
an  opposite  tendency  when  struck  by  the  gust. 
This  fin  may  be  made  sufficiently  large  to  over- 
come the  extra  lift  on  the  unshielded  wing  in 
addition,  when  the  negative  wing  tips  may  be 
dispensed  with — as  was  proposed  in  the  Ding- 
Sayers  monoplane. 

It  may  be  noted  that  vertical  fins  above  the 
centre  of  gravity  have  frequently  been  proposed, 
the  theory  being  that,  on  a  machine  tilting  side- 
ways there  would  be  a  tendency  to  slide  towards 
the  low  side,  and  that  the  consequent  air  pressure 
on  the  fin  would  push  the  machine  straight.  It  is 
obvious  that  this  fin  would  be  acted  on  by  side 
gusts  and  tend  to  increase  the  disturbance  due  to 
them.  It  is,  in  fact,  equivalent  in  most  ways  to  a 
simple  dihedral  angle,  but  inferior  in  the  degree 
of  stabilitv  obtainable. 


INHERENT  STABILITY 

DIRECTIONAL  STABILITY 

It  is  obviously  desirable  that  an  aeroplane  shall 
not  be  liable  to  be  deflected  from  its  course  by 
any  disturbance.  Now  a  purely  end-on  gust,  if 
uniform,  will  not  have  any  tendency  to  throw  the 
machine  off  its  course,  no  matter  what  its  force. 
In  the  case  of  a  side  gust  the  unshielded  wing  will 
have  an  increased  resistance  as  compared  with 
the  shielded  wing.  But  more  important  than  this 
is  the  effect  of  such  a  gust  on  the  body,  or  any 
other  side  surface,  such  as  fins  or  side  faces  of  a 
wing  at  a  dihedral  angle. 

To  secure  that  no  turning  tendency  shall  be 
produced  it  is  necessary  that  the  lines  of  action  of 
the  total  resultant  side  pressure  shall  act  through 
the  centre  of  gravity  of  the  machine.  Then  the 
only  effect  on  the  machine  will  be  bodily  motion 
sideways  without  any  turning  effect.  Unfortu- 
nately, the  centre  of  side  pressure  varies  in  position 
with  changes  in  the  direction  and  the  strength  of 
the  gust  ;  so  complete  balance  under  all  con- 
ditions is  impossible. 

Now  if  the  centre  of  side  pressure  is  forward  of 
the  CG,  the  nose  of  the  machine  will  turn  with 
the  gust,  and  the  machine  will  turn  down  wind, 
which  will  momentarily  reduce  its  air  speed.  If, 
on  the  contrary,  it  is  behind  the  CG,  the  tendency 
is  to  turn  up  wind  and  increase  the  air  speed. 
The  first  case  is  dangerous—  the  latter  safe,  there- 
fore it  is  desirable  to  keep  to  such  an  arrangement 
of  vertical  surfaces  as  will  always  keep  the  centre 
of  side  pressure  aft  of  the  CG. 


INHERENT  STABILITY 


But  the  most  important  aspect  of  this  question 
arises  when  the  machine  is  turning  under  the 
action  of  the  rudder.  Fig.  9  shows  this  case.  The 
rudder  of  the  machine  is  turned  to  the  left,  and  a 
pressure  (R)  acts  on  the  rudder,  tending  to  swing 
the  tail  of  the  machine  to  the  right.  Momentarily 
the  machine  moves  through  the  air  crab  wise, 
which  produces  a  side  pressure  (SP)  on  the  right- 
hand  side.  Under  these  two  pressures  the  machine 
commences  to  turn  in  the  curved  path  shown.  As 
soon  as  the  machine  starts,  actual  turning,  a  third 
force — centrifugal  force  (CF)  commences  to  act 
through  the  CG  of  the  machine,  and  towards  the 
outside  of  the  curve. 


INHERENT  STABILITY 

Now,  if  the  side  pressure  SP  acts  behind  the 
centrifugal  force — i.e.,  behind  the  CG — it  will  be 
seen  that  centrifugal  force  opposes  the  turning, 
and  when  the  rate  of  turning  has  reached  a  certain 
value  the  three  forces  are  in  balance  and  the 
machine  will  continue  turning  steadily.  If  the 
rudder  is  now  put  back  into  neutral,  R  disappears 
and  CF  and  SP  tend  to  take  the  machine  off  the 
turn,  and  both  of  them  disappear  as  soon  as  the 
machine  has  stopped  turning. 

But  suppose  SP  to  act  in  front  of  the  CG,  as  at 
the  dotted  arrow.  Then  CF  and  SP  themselves 
provide  a  tendency  to  turn  to  the  left,  added  to 
the  tendency  due  to  the  rudder,  and  instead  of 
reaching  a  steady  state  of  turning  the  machine 
will  turn  faster  and  faster.  Even  when  the  rudder 
is  put  back  to  neutral,  SP  and  CF  still  keep 
increasing  the  rate  of  turning.  As  a  matter  of  fact, 
as  the  rate  of  turning  increases  SP  tends  to  move 
further  forward,  and  to  increase,  hence  a  machine 
may  start  to  turn  with  SP  behind  the  CG,  and  as 
the  rate  of  turning  increases,  SP  may  move 
forward  till  it  is  in  front  of  the  CG,  and  may 
eventually  become  so  large  and  so  far  forward 
that  even  with  the  rudder  hard  over  in  the  opposite 
direction  the  turning  continues. 

This  is  the  explanation  of  the  spiral  nose  dive 
effect.  The  theory  of  the  elevator  acting  as  rudder 
when  the  machine  has  a  large  bank  does  not  ex- 
plain the  phenomenon,  as  unless  there  are  at  least 
two  forces  acting  independently  of  the  pressure 
on  the  control  surfaces  the  machine  will  cease  to 
turn  when  all  controls  are  placed  in  the  neutral 

90 


INHERENT  STABILITY 

position.  The  late  Lieut.  Parke's  experience  at 
Salisbury  in  1912  proved  that  this  is  not  the  case. 

Now  it  is  obvious  that  if  a  machine  slips  side- 
ways— say,  is  stalled,  rolls  over  to  one  side  and 
slides  downwards — that  a  side  pressure  similar 
to  SP  will  be  produced.  Also  the  inertia  of  the 
machine  will  produce  the  equivalent  of  CF,  or 
rather  will  produce  CF,  as  centrifugal  force  is 
only  an  inertia  effect,  and  the  turning  effect  due 
to  these  forces  appears.  Hence  the  spiral  may 
occur  without  any  use  of  the  rudder  at  all.  If  the 
direction  of  a  machine  is  changed,  extra  power 
has  to  be  supplied,  to  give  it  air  speed  in  its  new 
path,  and  if  the  turn  is  so  rapid  that  the  engine 
margin  of  power  is  not  sufficient  for  this  purpose 
— this  extra  work  must  be  done  by  gravity — the 
machine  must  dive,  and  the  faster  the  turn  the 
steeper  the  dive,  until  when  the  turning  rate  is 
such  that  a  force  equal  to  the  whole  weight  of  the 
machine  is  required  to  provide  the  air  speed  the 
machine  will  descend  vertically.  Therefore  this 
increasing  turning  effect  produces  that  most  deadly 
of  all  aeroplane  accidents — the  spiral  nose  dive. 

The  side  pressure  here  evidently  includes  that 
due  to  all  possible  causes  as  pressures  on  the  body, 
on  any  vertical  fins,  or  on  upturned  sides  of  wings. 
There  will  obviously  be  a  side  pressure  on  wings 
with  a  dihedral  when  turning,  or  on  flat  wings 
when  banked,  and  this  side  pressure  may  be  very 
large,  and  is  bound  to  act  not  far  from  the  centre 
of  gravity,  owing  to  the  position  of  the  wings. 
Hence,  as  far  as  possible,  this  side  pressure  must 
be  kept  small.  Obviously,  the  wings  themselves 

91 


INHERENT  STABILITY 

cannot  be  reduced,  but  swept -back  wings  with 
negative  tips  must  always  have  their  centre  of  side 
pressure  farther  back  relatively  to  their  centre  of 
lift  than  normal  wings.  Also  the  negative  tips  tend 
to  reduce  banking  on  turns  to  within  reasonable 
limits,  reducing  thereby  the  side  area  due  to  wings 
on  which  such  pressure  acts. 

Fins  beneath  the  centre  of  gravity,  when  acted 
on  by  the  side  pressure,  oppose  banking  with  the 
same  desirable  effect,  and  may  obviously  be  so 
arranged  as  to  have  their  own  centre  of  side  pres- 
sure as  far  aft  as  may  be  desired,  thus  securing 
this  essential  form  of  stability. 

With  fins  above  the  CG  the  tendency,  on  the 
contrary  is  to  increase  banking  on  turns,  or  to 
increase  the  tilt  due  to  a  side  gust,  and  therefore 
to  increase  the  total  value  of  side  pressure  possible, 
and  particularly  the  most  dangerous  component 
— that  on  tilted  wings — and  are  hence  objection- 
able and  even  dangerous,  as  tending  to  produce 
the  very  catastrophe  for  which  they  have  been 
proposed  as  a  remedy,  unless  made  extremely 
large  and  placed  very  far  back. 

At  the  time  at  which  the  preceding  statements 
on  spiral  instability  were  written  nothing  had 
been  published  on  this  subject  (so  far  as  is  known 
to  the  writer),  with  the  exception  of  certain  para- 

fraphs  in  "  Aerodonetics  "  (Lanchester,  "  Aerial 
light,5'  Vol.  z) ;  but  in  the  meantime,  Mr.  Bair* 
stow  has  dealt  with  the  matter  in  his  lecture  before 
the  Aeronautical  Society  (January  2ist,  "  The 
Stability  of  Aeroplanes  ").  Both  Mr.  Lanchester 
and  Mr.  Bairsto'w'  claim  that  the  cure  for  directional 

92 


INHERENT  STABILITY 


93 


INHERENT  STABILITY 

instability  lies  in  a  forward  centre  of  side  pressure, 
and  apparently  prove  their  assertions  by  experi- 
ments with  models,  thus  definitely  contradicting 
the  writer's  conclusions.  It  may  be  as  well,  there- 
fore ,  to  go  into  this  question  a  little  more  completely. 

In  Fig.  10, 1  is  a  replica  of  Fig.  9,  except  that  it 
shows  how  the  centre  line  of  the  machine  deviates 
from  the  tangent  to  its  circular  path,  which  is  the 
momentary  line  of  flight — i.e.,  that  it  "  crabs  " 
slightly,  thereby  producing  the  side  pressure,  SP. 
II  shows  the  case  of  the  machine  with  the  forward 
centre  of  side  pressure.  In  this  case,  as  soon  as 
the  rudder  is  put  slightly  over,  "  crabbing  "  com- 
mences, and  the  forward  side  pressure  swings  the 
machine  still  further  askew  until  the  angle  be- 
tween AB  (the  momentary  line  of  flight)  and  the 
centre  line  of  the  machine  is  greater  than  that 
between  the  centre  line  of  the  machine  and  of  the 
rudder.  The  force  on  the  rudder  then  becomes 
reversed  and  acts  from  the  outside,  so  that  we 
again  have  SP  and  R  acting  in  opposition,  though 
their  respective  roles  are  reversed.  The  machine, 
as  long  as  the  rudder  is  held  in  such  a  position, 
will  turn  steadily  at  a  definite  radius,  with  the 
rudder  checking  the  tendency  to  spin. 

Now  in  a  model  aeroplane  the  rudder  is  actually 
a  fixed  surface,  hence  this  arrangement  apparently 
gives  the  required  stability.  But  in  any  actual 
aeroplane  it  is  not  fixed,  and  may  be  put  into  a 
position  of  no  resistance  to  turning,  and  will  take 
that  position  itself  if  a  rudder  wire  breaks  or  the 
pilot's  foot  slips  from  the  bar,  when  the  machine 
becomes  completely  unstable  and  spirals  violently. 

94 


INHERENT  STABILITY 

AN  IMPORTANT  OVERSIGHT. 

A  rudder  is  not  a  fixed  surface  and  must  not  be 
counted  on  as  such  in  a  full-sized  machine — 
although  it  usually  is,  and  acts  as  such,  in  a  model. 

It  may  be  remembered  that  Mr.  Bairstow  re- 
ferred to  marked  lateral  oscillations  in  his  "  stable" 
models.  What  happens  in  this  case  is  that  the 
model,  on  tilting  sideways,  slides  down  slightly 
and  produces  the  side  pressure  SP,  which  tends 
to  spiral  it  to  the  other  side.  This  tendency  is 
checked  by  the  damping  of  the  very  large  fins  and 
by  the  reversed  rudder  action — but  with  a  free 
rudder  this  model  would  spiral  and  nose-dive 
towards  the  (original)  high  side  after  each  lateral 
disturbance  ;  while  the  machine  with  the  side 
area  aft  merely  dives  and  swings  towards  the  low 
side  without  any  tendency  to  spiral  continuously. 

Mr.  Bairstow's  "  unstable  "  model — produced 
by  removing  the  front  fin — was  in  the  condition 
already  referred  to  in  which  the  centre  of  side 
pressure  is  at  the  commencement  of  a  turn  behind 
the  CG,  but  moves  forward  as  the  turn  progresses. 
This  change  over  is  extremely  dangerous — much 
more  so  than  the  really  unstable  condition,  with 
the  permanently  forward  centre  of  side  pressure, 
as  this  latter,  on  account  of  the  permanent  nega- 
tive pressure  on  the  rudder-bar,  gives  the  pilot  a 
continual  warning  that  the  machine  is  trying  to 
spin,  while  the  change  over  is  sudden  and  dis- 
concerting. 


95 


INHERENT  STABILITY 

A  WARNING   AGAINST  ASSUMPTIONS. 

From  the  foregoing  it  would  appear  as  if  in 
order  to  secure  complete  immunity  from  direct- 
ional instability,  it  is  only  necessary  to  supply  an 
ample  rear  fin,  and  that  it  is  desirable  to  reduce 
the  dihedral  style  to  as  small  a  value  as  is  consonant 
with  the  requirements  of  pure  lateral  stability  so 
as  to  avoid  undue  banking. 

Unfortunately  the  case  is  somewhat  more  com- 
plex. In  order  to  be  able  to  turn  without  excessive 
:'  crabbing,"  or  skidding  sideways,  it  is  necessary 
that  the  side  pressure  at  a  small  rate  of  movement 
sideways  shall  balance  the  rudder  force  and  centri- 
fugal force. 

Now  if  the  centre  of  side  pressure  is  very  close 
to  the  centre  of  gravity,  and  the  side  pressure  is 
nearly  equal  to  the  centrifugal  force  in  magnitude, 
there  will  only  be  required  a  quite  small  rudder 
force  to  provide  the  required  state  of  balance. 
But  if  the  centre  of  side  pressure  be  very  far  aft 
of  the  centre  of  gravity  the  rudder  force  required 
to  produce  a  state  of  balance  will  be  greatly  in- 
creased. That  is  to  say  that  the  pilot  will  have  to 
make  greater  muscular  efforts  to  steer  the  machine 
and  the  machine  will  also  respond  less  rapidly  and 
easily  to  the  rudder. 

Also,  since  centrifugal  force  increases  as  the 
radius  of  turning  decreases,  it  is  necessary  that  on 
sharp  turns  both  the  side  pressure  and  the  rudder 
force  should  increase.  The  rudder  force  will  in- 
crease with  the  increase  of  the  angle  to  which  the 
rudder  is  put  over,  but  to  increase  the  side  pressure 


INHERENT  STABILITY 

either  the  rate  of  motion  sideways,  or  the  side 
area,  must  increase.  As  it  is  desirable  to  keep  the 
sideways  motion  as  small  as  possible  it  is  neces- 
sary to  increase  the  actual  side  area,  and  that  can 
only  be  done  by  increased  banking,  thus  making 
the  inclined  faces  of  the  wings  effective  for  this 
purpose. 

For  these  two  reasons  a  machine  which  shall  be 
easily  steered  can  only  be  made  by  approaching 
very  closely  to  the  condition  in  which  the  centre 
of  side  pressure  corresponds  with  the  centre  of 
gravity  and  the  margin  between  this  condition  and 
one  of  instability  is  very  narrow. 


INHERENT  STABILITY 

EXPERIMENTS  NEEDED 

In  this  connection  it  may  be  remarked  that  a 
series  of  experiments  are  desirable  on  the  be- 
haviour of  bodies  of  the  form  used  as  aeroplane 
fuselages  or  nacelles,  and  of  flat  surfaces  moving 
in  a  curved  path  and  at  a  slight  angle  to  that  path. 

Very  little  is  known  on  this  subject,  but  there 
is  much  evidence  showing  that  differences  in 
body  form  may  completely  alter  the  behaviour 
of  a  machine  in  this  respect,  and  one  might  hazard 
a  guess  that  in  Fig.  n  the  centre  of  side  pressure 
of  A  would  occupy  a  considerably  more  forward 
position  than  that  of  B  when  acted  on  by  a  wind 
as  indicated  by  the  arrows,  and  that  a  machine 
with  a  fuselage  or  nacelle  entry  such  as  A  might 
be  unstable,  whereas  an  otherwise  identical 
machine  with  a  body  entry  such  as  B  might  be 
stable. 


C 


98 


INHERENT  STABILITY 

STABILITY  IN  VARIOUS  TYPES. 

Having  now,  if  not  briefly,  at  least  rather 
hastily,  considered  the  question  of  inherent 
stability  in  all  its  more  important  aspects,  we  will 
consider  one  or  two  types  of  machine  in  order  to 
notice  to  what  extent  the  various  desirable  features 
may  be  combined,  and  what  disadvantages  from 
other  points  of  view  sxich  combinations  may  have. 

1.  Machines  with  planes  at  right  angles  to  the 
line  of  flight,  with  tapered  and  or  "  washed  out fl 
planes.  Appreciable  reduction  in  the  disturbance 
due  to  side  gusts.  Combined  with  the  longitudinal 
V,  and  a  proper  vertical  position  of  the  CG,  both 
longitudinal  or  lateral  stability  may  be  obtained, 
with  a  fair  degree  of  steadiness.  With  a  correct 
disposition  of  side  surfaces  ensuring  that  the  centre 
of  side  pressure  is  always  aft  of  the  centre  of 
gravity,  immunity  from  the  uncontrollable  spiral 
nose  dive  is  secured. 

2.  Machines  as  above  with  negative  wing  tips. 
Partial  or  complete  neutralisation  of  disturbing 
forces  due  to  side  gusts,  reduction  of  tendency  to 
overbanking  on  turns,  leading  to  further  reduction 
of  risk  of  spiral  nose  dives.  In  combination  with 
the  longitudinal  V,  correct  position  of  CG,  etc., 
has  the  same  good  qualities  as  No.  i,  with  an  en- 
hanced degree  of  lateral  steadiness  and  immunity 
from  spiral  dives. 

In  both  the  above  forms  the  tendency  is  rather 
to  increase  the  sensitiveness  of  the  machine  to  the 
warp  while  longitudinal  controls  are  normal, 

3.  Machines  having  negative  tips  and  swept-back 

99 


INHERENT  STABILITY 

wings.  These  give  the  same  lateral  steadiness 
as  the  above,  a  greater  and  possibly  a  complete 
immunity  from  side  slip,  owing  to  the  centre  of 
side  pressures  on  such  wings  being  aft  of  the 
centre  of  normal  pressure,  and  have  in  the  plane 
themselves  a  longitudinal  V  which  can  be  made  to 
provide  longitudinal  stability.  As  with  previous 
classes,  lateral  controls  are,  if  anything,  unusually 
sensitive. 

If,  like  the  Dunne,  the  planes  are  relied  on  for 
longitudinal  stability,  and  tail  planes  and  booms 
are  not  used,  they  may  be  more  sensitive  to 
elevator  control  than  normal  machines,  owing  to 
the  better  concentration  of  weights. 

As  with  the  other  forms,  the  stability  due  to 
the  wings  themselves  may  be  supplemented  by 
any  of  the  other  methods  of  stabilising  already 
considered.  In  practice,  machines  of  this  type 
show  themselves  to  be  safe,  steady  and  sensitive 
to  control.  It  must  be  noted  that  all  machines 
with  negative  tips  must  lose  in  efficiency  some- 
where, as  the  head  resistance  of  the  part  of  the 
wing  beyond  the  non-lifting  line  not  only  is 
accompanied  by  no  lift,  but  by  an  actual  negative 
lift.  Actually  owing  to  several  causes — one  being 
the  large  value  of  dead  resistance,  i.e.,  body, 
chassis,  etc. — this  loss  in  efficiency  is  not  pro- 
hibitive, some  machines  with  negative  tips  having 
better  gliding  angles  than  some  not  so  provided. 

4.  Machines  in  which  a  dihedral  angle  and  a 
low  centre  of  gravity  are  relied  on  for  lateral 
stability.  In  this  case  disturbance  due  to  lateral 
gusts  is  great ;  also,  when  turning  a  corner,  there 

100 


INHERENT  STABILITY    .-, 

is  a  tendency  to  overbank,  owing  to  centrifugal 
force  acting  below  the  centre  of  side  pressure, 
hence  risk  of  side  slip.  By  the  adoption  of  vertical 
fins  below  the  centre  of  gravity  both  these  dis- 
advantages are  overcome.  By  suitable  proportion- 
ing of  the  fin,  i.e.,  by  keeping  its  centre  of  side 
pressure  back  far,  immunity  from  spiral  diving 
can  be  obtained.  This  arrangement  can,  of  course, 
be  combined  with  the  longitudinal  V,  giving,  as 
far  as  can  be  predicted,  as  good  results  as  any 
combination  yet  tried.  In  this  case  no  interference 
with  the  elevator  controls  occurs.  With  the  fins 
some  damping  of  the  warp  and  rudder  controls 
is  inevitable — owing  to  the  large  fins  necessary. 
This  damping,  however,  could  not  be  greater 
than  about  one-tenth  of  the  damping  due  to  other 
essential  parts  of  the  machine,  which  in  practice 
would  be  inappreciable.  No  example  of  this  type 
has  been  completed,  but  the  behaviour  of  certain 
deep-bodied  monoplanes,  notably  the  R.E.P.  and 
Clement-Bayard,  tend  to  confirm  the  value  of 
this  method. 

There  are  doubtless  other  forms  of  machine 
claiming  inherent  stability,  but  little  or  nothing 
is  known  as  to  their  performance  or  of  the  ideas 
which  have  prompted  their  designers. 

It  will  be  noted  that  the  question  of  the  con- 
trollability of  the  various  types  of  stable  machines 
has  been  referred  to,  and  that  very  little  dis- 
advantage as  compared  with  normal  machines 
has  been  admitted.  It  is  assumed  that  the  machine 
has  been  arranged  to  be  stable  with  all  controls 
in  the  normal  condition*  and  it  can  be  easily  seen 

101 


INHERENT  STABILITY 

that  if  sufficiently  powerful  controls  are  fitted 
the  inherent  stability  may  be  largely  or  com- 
pletely destroyed. 

For  instance,  if  a  sufficiently  powerful  rudder 
is  held  hard  over,  any  machine  must  spiral  and 
nose  dive.  But,  except  in  the  case  of  a  jammed 
control,  this  does  not  matter,  as  the  pilot  can  at 
once  stop  the  effect,  by  leaving  the  rudder  free, 
provided  the  machine  has  the  proper  disposition 
of  side  surfaces.  Therefore  the  pilot  can  use  his 
controls  to  any  extent  in  an  emergency,  at  the 
expense,  of  course,  of  a  dive,  with  the  certainty 
that  after  the  removal  of  the  control  force  the 
machine  will  return  to  the  normal  conditions. 
This  is  not  true  of  an  unstable  machine — as 
shown  in  the  section  on  spiral  dives.  A  large 
amount  of  the  prejudice  on  this  head  arises  from 
the  confusion — already  pointed  out — between  the 
slow  movements  of  the  machine  whose  weights 
are  widely  distributed,  and  the  lively  motion  of 
the  one  in  which  they  are  concentrated.  The  first 
are  usually  credited  with  a  large  amount  of 
stability  by  those  who  see  them  in  flight.  They 
are  inevitably  slow  in  answering  their  controls, 
hence  the  myth  that  a  stable  machine  does  not 
answer  well  to  controls.  Actually  this  quality 
from  which  the  steadiness  arises  is  adverse  to 
stability  and  the  objection  is  groundless. 


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